Publications

2026

• Jianning Wang, Robert Ślepaczuk, Paweł Sakowski (2026), MLP-Initialized Reinforcement Learning for Exit Timing in SPX Short-Straddle Portfolios, arXiv preprint arXiv:2610.13126

  This paper studies exit timing for SPX short-straddle portfolios using a two-stage supervised and reinforcement-learning framework. Historical episodes first generate ex-post optimal hold/exit labels for training a multilayer perceptron (MLP) using only contemporaneously available state variables at deployment. The trained MLP then initializes reinforcement-learning actors that are fine-tuned with a risk-aware trading reward. Out-of-sample evaluation over 2024-2026 shows that the supervised MLP substantially outperforms passive holding and representative fixed-time and profit-and-loss-based exit rules. Across seven independent seeds, MLP-initialized Actor-Critic averages 37.54% cumulative return and a Sharpe ratio of 1.705, compared with 35.01% and 1.651 for the supervised MLP. Actor-Critic trained from scratch averages only 0.18% return. These findings show that oracle-guided supervised learning provides a stable foundation for reward-based policy fine-tuning in a sparse and path-dependent option-exit problem.

• Maciej Wysocki (2026), Sizing the risk: Kelly, VIX, and hybrid approaches in put-writing on index options, Knowledge-Based Systems, Volume 348, Article 116331

  This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility generally exceeds realized volatility, the practical implementation of short-dated volatility-selling strategies remains underdeveloped in the literature. To address the non-linear, fat-tailed risks inherent in put-writing, this study introduces a novel algorithmic framework for dynamic position sizing — a hybrid architecture that integrates Monte Carlo-derived Kelly sizing with real-time VIX-regime scaling. Using at-the-money and out-of-the-money SPXW options with expirations ranging from 0 to 5 days, the analysis explores a broad design space, including moneyness levels, volatility estimators, and memory horizons. The results demonstrate that ultra-short-dated, far out-of-the-money options deliver superior risk-adjusted returns. The hybrid sizing method consistently balances return generation with robust drawdown control, particularly during low-volatility periods such as those observed in 2024. Ultimately, this research offers new insights into volatility harvesting through a novel adaptive sizing approach that responds to shifting market regimes. It provides practical guidance on constructing short-dated option strategies that can withstand diverse market environments. These findings have direct applications for institutional investors seeking to enhance portfolio efficiency through systematic exposure to volatility premia.

• Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk (2026), Alternative loss function in evaluation of algorithmic investing strategies based on transformer models, Pattern Recognition Letters, Volume 203, Pages 170-176

  The proper design and architecture of testing machine learning models, especially in their application to quantitative finance problems, is crucial. The most important aspect of this process is selecting an adequate loss function for training, validation, estimation purposes, and hyperparameter tuning. Therefore, in this research, through empirical experiments on equity and cryptocurrency assets, we apply the Mean Absolute Directional Loss (MADL) function, which is more adequate for optimizing forecast-generating models used in algorithmic investment strategies. The MADL function results are compared between Transformer, LSTM, GRU, and CNN models, and we show that in almost every case, Transformer results are significantly better than those obtained by benchmark models.

• Filip Stefaniuk, Robert Ślepaczuk (2026), A neural network informer in algorithmic investment strategies on high-frequency bitcoin data, Expert Systems with Applications, Volume 317, Article 131599

  The article investigates the usage of Informer architecture for building automated trading strategies for high frequency Bitcoin data. Three strategies using Informer model with different loss functions: Root Mean Squared Error (RMSE), Generalized Mean Absolute Directional Loss (GMADL) and Quantile loss, are proposed and evaluated against the Buy and Hold benchmark and two benchmark strategies based on technical indicators. The evaluation is conducted using data of various frequencies: 5 minute, 15 minute, and 30 minute intervals, over the 6 different periods. Although the Informer-based model with Quantile loss did not outperform the benchmark, two other models achieved better results. The performance of the model using RMSE loss worsens when used with higher frequency data while the model that uses novel GMADL loss function is benefiting from higher frequency data and when trained on 5 minute interval it beat all the other strategies on most of the testing periods. The primary contribution of this study is the application and assessment of the RMSE, GMADL and Quantile loss functions with the Informer model to forecast future returns, subsequently using these forecasts to develop automated trading strategies. The research provides evidence that employing an Informer model trained with the GMADL loss function can result in superior trading outcomes compared to the buy-and-hold approach

• Maciej Wysocki (2026), Harvesting the Volatility Risk Premium: A Learning-to-Rank Approach, arXiv preprint arXiv:2608.24786

  This paper develops the first end-to-end application of cross-sectional learning-to-rank to the S&P 500 weekly options (SPXW) zero-day-to-expiration surface, integrated with margin-aware position sizing, an abstention rule driven by model uncertainty, and a strict out-of-time integrity check. A LightGBM LambdaRank ranker scores a daily nine-strategy cross-section composed of eight delta-targeted short-put positions and a \textit{SKIP} candidate, trained against a path-aware Sortino-on-bars label computed at one-minute resolution. The framework is evaluated under index-option margin requirements, a tiered fee schedule, and bid-to-mid execution assumptions across a four-window walk-forward over 2021-2024 and a strictly held-out 2025 out-of-time slice. Seven sizing methods produce out-of-time annualized Sharpe ratios between 4.31 and 5.76, with the headline method reaching a Probabilistic Sharpe Ratio of 0.964 and a sample-period maximum drawdown of -2.28%, on a single hold-out year against a walk-forward range of 1.90 to 3.11. Out of time, every method exceeds three passive benchmarks (CBOE PUT, CBOE WPUT, SPX buy-and-hold) by at least 3.84 in Sharpe ratio and five internal selection baselines by at least 3.69. A two-by-two ablation of the confidence gate against the tail-risk features places 5.05 of the 5.59 out-of-time Sharpe gap over the CBOE PUT with the ranker and the selection layer, the two risk controls adding 0.54 between them. On walk-forward, where the gate binds, neither control comes close to the headline alone and their interaction supplies most of the result. A fifteen-group feature ablation shows that removing the multiplicative regime interactions collapses walk-forward statistical confidence.

• Łukasz Adamski, Robert Ślepaczuk (2026), When the Fed Speaks: Dynamics and Forecasts of the Volatility Surface, arXiv preprint arXiv:2608.10693

  Our primary goal is to forecast and empirically examine the evolution of the implied volatility (IV) surface, with particular focus on the dates of scheduled meetings of the Federal Open Market Committee (FOMC). Firstly, we check if IV increases before the announcement and if thes effect is stronger for short-dated, out-the-money (OTM) options in high volatility regimes. In the second part, we turn the focus to verifying if the ML framework can beat the benchmark random walk in forecasting this effect. A feature related to dates of scheduled FOMC meetings augments the model, which allows us to discover if it can learn the effect of elevated pre-announcement uncertainty. Our contribution relies mainly on the quantitative prediction of the pre-announcement effect and the inclusion of exogenous information inside the ML framework used for the IV surface forecasting. It is also on of the first attempts to apply ML models directly on the IV surface without relying on dimensionality reduction. To achieve this, we employ a convolutional two-dimensional LSTM model, which is capable of learning spatio-temporal signals in the surface. Our analysis reveals that the edge of the ML framework can be limited due to the noisy characteristics of the IV surface. Nevertheless, our study reinforces the perspective that ML models can effectively forecast the IV surface also during abnormal days.

• Isidro Moroso Varona, Jakub Michańków, Paweł Sakowski (2026), Randomized Neural Networks for estimation of exposure profiles and Credit Valuation Adjustment (CVA) for American Equity Options, arXiv preprint arXiv:2606.24309

  This paper studies the use of randomized neural networks for the estimation of exposure profiles and unilateral CVA of American options within a Monte Carlo framework. The analysis is carried out separately under both Black-Scholes and Heston dynamics, combining American option valuation, expected exposure and potential future exposure estimation, and unilateral CVA calculation with portfolio netting effects. The numerical experiment compares this approach with the classical Least-Squares Monte Carlo (LSM) used as a benchmark in both low-dimensional single-asset and high-dimensional multi-asset scenarios, and also includes a path convergence test and a sensitivity analysis. The results show that the randomized feedforward neural network approach preserves convergence to the LSM benchmark when it is extended from pricing to exposure and CVA estimation, while its main advantage appears in high-dimensional problems, where it scales more efficiently and leads to lower computational cost. These results support the use of randomized neural networks as a useful alternative for exposure and CVA estimation in high-dimensional American-style options.

• Xinyue Fang, Robert Ślepaczuk (2026), Volatility Forecasting and Return Prediction under Market Regimes: Evidence from High-Frequency Chinese Equity Data, arXiv preprint arXiv:2606.09478

  This study investigates whether regime-dependent volatility forecasting and machine-learning-based return prediction can be jointly integrated to improve both statistical forecasting performance and economic strategy outcomes in equity markets. Using high-frequency CSI 300 Index data from 2005 to 2023, a sequential twostage framework is developed. In the first stage, realized volatility is modeled using regime-augmented HARQ specifications combined with Markov-switching GJR-GARCH filtering to capture long-memory dynamics, asymmetry, and structural market regimes. In the second stage, volatility forecasts, regime indicators, and return-related predictors are incorporated into an XGBoost return-prediction model estimated through a strictly walk-forward out-of-sample procedure. The empirical results demonstrate that regime-aware volatility forecasting consistently outperforms baseline HARQ models across forecast evaluation metrics and is generally supported by formal forecast comparison tests. In contrast, return predictability remains weak, state-dependent, and concentrated primarily in low-volatility regimes. Although naive predictive trading strategies generally fail after accounting for realistic transaction costs, carefully designed implementations incorporating volatility scaling, low-volatility gating, threshold calibration, and turnover controls can improve defensive economic performance. The findings suggest that the practical value of predictive systems in financial markets may depend less on generating strong unconditional return forecasts and more on transforming weak state-dependent signals into economically robust portfolio allocation rules. Overall, the study contributes by integrating econometric volatility modeling, regime classification, machine-learning return prediction, and implementation realism within a unified framework.

• Damian Lebiedź, Robert Ślepaczuk (2026), Dynamic Multi-Pair Trading Strategy in Cryptocurrency Markets with Deep Reinforcement Learning, arXiv preprint arXiv:2606.04574

  This study aims to determine whether the application of Deep Reinforcement Learning (DRL) as a specialized execution overlay can enhance pair trading in highly volatile cryptocurrency markets. Although classical implementations of the strategy have proven successful in traditional equities, they frequently exhibit rigidity and suffer from severe divergence risks when applied to high-variance environments. To address this need, this research introduces novel concepts. To construct a robust system, we developed a hierarchical “Filter-then-Rank” pair selection methodology and a proprietary “Fixed Risk, Adaptive Mean” execution model. The system employs a Proximal Policy Optimization (PPO) agent with a Long Short-Term Memory (LSTM) layer to govern execution decisions within strict deterministic risk management boundaries. Evaluated on 1-hour interval data from the Binance USD-M Futures market, the optimized RL policy achieved an out-of-sample performance that substantially outperformed the heuristic baseline. A stationary circular block bootstrap robustness check confirms that the agent’s risk-adjusted outperformance is statistically significant at the 10 percent level. Although falling marginally short of the stricter 5 percent threshold, this result highlights the extreme idiosyncratic variance characteristic of digital assets. Ultimately, this thesis contributes to the quantitative finance literature by introducing a hybrid architecture that combines statistical arbitrage with DRL execution policies. Furthermore, it delivers a novel framework for safe reinforcement learning via deterministic shielding, proving that anchoring a neural policy to statistically robust boundaries successfully mitigates severe divergence risks.

• Andrei Bysik, Robert Ślepaczuk (2026), Machine Learning-Based Bitcoin Trading Under Transaction Costs: Evidence From Walk-Forward Forecasting, arXiv preprint arXiv:2606.00060

  This paper investigates whether machine learning forecasts of hourly BTC-USDT returns can be converted into economically meaningful trading performance after transaction costs. Using approximately 70,000 hourly observations from 2018-2026, XGBoost, LSTM, and iTransformer are evaluated in a 27-fold walk-forward protocol. All three models produce positive gross trading performance in selected configurations, but naive sign-based strategies fail once transaction costs of ten basis points are imposed. A cost-aware execution filter, which prevents trades only when the forecast magnitude exceeds a transaction-cost-based threshold, sharply reduces turnover and restores profitability in selected configurations. The strongest long-only XGBoost strategy produces annualised returns above 65% with a Sharpe ratio above one. Additional tests show that technical indicators improve performance in selected cases, EGARCH-derived features do not provide uniformly robust gains, and XGBoost is descriptively stronger than the neural alternatives, although bootstrap evidence does not support formal statistical dominance. Loss-function and model-selection effects are secondary and statistically fragile. The results show that the main obstacle in hourly cryptocurrency trading is not only weak predictability, but also the way forecasts are converted into trades.

• Kamil Kashif, Robert Ślepaczuk (2026), Deep Reinforcement Learning Framework for Diversified Portfolio Management Across Global Equity Markets, arXiv preprint arXiv:2605.17307

  This study develops and evaluates a deep reinforcement learning framework for dynamic portfolio allocation across global equity markets. The Soft Actor-Critic algorithm is used to learn continuous portfolio weights within a Markov Decision Process, incorporating transaction costs, turnover penalties, and diversification constraints into the reward function. Five model configurations are compared, varying in reward formulation, policy structure (flat versus hierarchical Dirichlet), portfolio constraints, and temporal encoder (LSTM versus Transformer), and evaluated via walk-forward optimization across sixteen out-of-sample folds spanning 2003-2026 on the Nasdaq-100, Nikkei 225, and Euro Stoxx 50. Results show that RL strategies achieve competitive risk-adjusted performance primarily in the Euro Stoxx 50, where statistically significant abnormal returns are observed, but the central hypothesis is only partially confirmed: no strategy achieves statistically significant excess returns relative to Buy and Hold under HAC-robust inference across all markets. Regime analysis reveals that RL adds the most value during periods of elevated uncertainty, while ensemble aggregation across markets improves risk-adjusted performance and confirms the benefits of geographic diversification.

• Maciej Wysocki, Elżbieta Wysocka, Marek Giergiczny (2026), Forecasting Timber Prices in Volatile Markets: An Evaluation of Model Complexity and Temporal Frequency, SSRN Working Paper

  Accurate timber price forecasting is crucial for effective forest management and a strategic response to changing commodity markets. This study quantifies the forecasting accuracy of univariate statistical and machine-learning methods at weekly, monthly, and quarterly time intervals using price data on Polish pine sawlogs and pulpwood. We evaluate Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), Dynamic Harmonic Regression (DHR), a Light Gradient Boosting Machine (LightGBM), and naive baselines. A major practical issue discussed is whether temporally aggregating weekly forecasts yields better accuracy than direct monthly modeling. Theoretical analysis shows that direct monthly modeling is almost always better than upward aggregation, since higher-frequency data is statistically noisier, which leads to degradation of predictive accuracy at lower frequencies. In a purely univariate context, statistical models perform better than the LightGBM model, which indicates that, in order to be able to reveal meaningful signals, machine learning models need access to exogenous macroeconomic variables. Furthermore, we quantify model resilience during the COVID-19 structural market break. While all models failed to predict the unprecedented price surge, the simple naive baseline adapted to newly established price levels much faster than parametric models retaining outdated pre-shock distributions. Ultimately, for long-term strategic planning, direct monthly modeling using ARIMA or a naive baseline remains the most reliable and efficient approach for forestry organizations.

• Maciej Wysocki, Wiktor Budziński, Marek Giergiczny, Robert Ślepaczuk (2026), Multi-Horizon Machine Learning Forecasts of Timber Prices with Macroeconomic and International Drivers, SSRN Working Paper

  Timber price forecasting is critical for production planning, contract design, and investment decisions across the construction and pulp and paper industries. The Polish timber market presents a distinctive institutional setting in which the State Forests (Lasy Państwowe) operate as a near-monopoly in timber supply, shaping auction outcomes and market dynamics to an extent unmatched elsewhere in Europe. This system amplifies both local constraints and macro-regional shocks transmitted through trade links with Germany and Finland. Timber prices in Poland are strongly influenced by macroeconomic and policy factors, including inflation, interest rates, energy costs, and EU climate initiatives such as the Fit-for-55 package, as well as by exogenous shocks like the COVID-19 pandemic and the 2022–2023 energy crisis. We construct weekly price series (2009–2025) for two major pine assortments — w_standard (sawlogs) and S_S2A (pulpwood) - from e-Drewno auction data and augment them with international timber prices, macro-financial indicators, and housing market variables. A hierarchical feature-selection pipeline combining ridge regression, LightGBM-based importance measures, recursive elimination, and forward selection identifies relevant autoregressive and exogenous predictors with lags of up to 52 weeks. Forecasts are generated using a direct multi-horizon LightGBM approach that trains separate models for each of 26 forecast weeks. Our results show that incorporating macroeconomic and international variables substantially improves medium-term forecast accuracy relative to autoregressive baselines. The importance of explanatory factors differs across assortments, reflecting their distinct industrial uses and sensitivity to economic cycles. The proposed pipeline provides an interpretable, operational framework for rolling updates of timber price forecasts in a quasi-monopolistic market shaped by domestic policy and European climate objectives.

• Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk (2026), Generalized Mean Absolute Directional Loss for Machine Learning Trading Models, SSRN Working Paper

  The article presents and evaluates a custom loss function designed specifically for machine learning models used in algorithmic trading. Regardless of the selected asset class and the level of model complexity, the proposed Generalized Mean Absolute Directional Loss (GMADL) function produces superior results and has better numerical properties during optimization than classic regression and classification based loss functions. Better results correspond to higher risk-weighted returns based on buy and sell signals derived from forecasts generated by models trained using GMADL. In practice, GMADL improves model evaluation by aligning the learning objective with trading performance rather than generic error minimization or simple directional accuracy. Through additional parameterization, GMADL provides a flexible mechanism for adjusting the loss’s sensitivity to different return magnitudes, which affects model evaluation consistency across various market regimes. This improves the selection of model configurations that are more consistent with performance-based criteria. Moreover, the implementation uses robust machine learning tools, including frameworks for hyperparameter tuning, architecture testing, and walk-forward optimization, to provide robust and scalable model evaluation across real-world financial data from different asset classes.

• Szymon Lis, Robert Ślepaczuk, Paweł Sakowski (2026), Overreaction as an indicator for momentum in algorithmic trading: A Case of AAPL stocks, arXiv preprint arXiv:2602.18912

  This paper investigates whether short-term market overreactions can be systematically predicted and monetized as momentum signals using high-frequency emotional information and modern machine learning methods. Focusing on Apple Inc. (AAPL), we construct a comprehensive intraday dataset that combines volatility normalized returns with transformer-based emotion features extracted from Twitter messages. Overreactions are defined as extreme return realizations relative to contemporaneous volatility and transaction costs and are modeled as a three-class prediction problem. We evaluate the performance of several nonlinear classifiers, including XGBoost, Random Forests, Deep Neural Networks, and Bidirectional LSTMs, across multiple intraday frequencies (1, 5, 10, and 15 minute data). Model outputs are translated into trading strategies and assessed using risk-adjusted performance measures and formal statistical tests. The results show that machine learning models significantly outperform benchmark overreaction rules at ultra short horizons, while classical behavioral momentum effects dominate at intermediate frequencies, particularly around 10 minutes. Explainability analysis based on SHAP reveals that volatility and negative emotions, especially fear and sadness, play a central role in driving predicted overreactions. Overall, the findings demonstrate that emotion-driven overreactions contain a predictable structure that can be exploited by machine learning models, offering new insights into the behavioral origins of intraday momentum and the interaction between sentiment, volatility, and algorithmic trading.

• Tomasz Mroziewicz, Robert Ślepaczuk (2026), A novel approach to trading strategy parameter optimization using double out-of-sample data and walk-forward techniques, arXiv preprint arXiv:2602.10785

  This study introduces a novel approach to walk-forward optimization by parameterizing the lengths of training and testing windows. We demonstrate that the performance of a trading strategy using the Exponential Moving Average (EMA) evaluated within a walk-forward procedure based on the Robust Sharpe Ratio is highly dependent on the chosen window size. We investigated the strategy on intraday Bitcoin data at six frequencies (1 minute to 60 minutes) using 81 combinations of walk-forward window lengths (1 day to 28 days) over a 19-month training period. The two best-performing parameter sets from the training data were applied to a 21-month out-of-sample testing period to ensure data independence. The strategy was only executed once during the testing period. To further validate the framework, strategy parameters estimated on Bitcoin were applied to Binance Coin and Ethereum. Our results suggest the robustness of our custom approach. In the training period for Bitcoin, all combinations of walk-forward windows outperformed a Buy-and-Hold strategy. During the testing period, the strategy performed similarly to Buy-and-Hold but with lower drawdown and a higher Information Ratio. Similar results were observed for Binance Coin and Ethereum. The real strength was demonstrated when a portfolio combining Buy-and-Hold with our strategies outperformed all individual strategies and Buy-and-Hold alone, achieving the highest overall performance and a 50 percent reduction in drawdown. A conservative fee of 0.1 percent per transaction was included in all calculations. A cost sensitivity analysis was performed as a sanity check, revealing that the strategy’s break-even point was around 0.4 percent per transaction. This research highlights the importance of optimizing walk-forward window lengths and emphasizing the value of single-time out-of-sample testing for reliable strategy evaluation.

• Bartosz Bieganowski, Robert Ślepaczuk (2026), Explainable Patterns in Cryptocurrency Microstructure, arXiv preprint arXiv:2602.00776

  We document stable cross-asset patterns in cryptocurrency limit-order-book microstructure: the same engineered order book and trade features exhibit remarkably similar predictive importance and SHAP dependence shapes across assets spanning an order of magnitude in market capitalization (BTC, LTC, ETC, ENJ, ROSE). The data covers Binance Futures perpetual contract order books and trades on 1-second frequency starting from January 1st, 2022 up to October 12th, 2025. Using a unified CatBoost modeling pipeline with a direction-aware GMADL objective and time-series cross validation, we show that feature rankings and partial effects are stable across assets despite heterogeneous liquidity and volatility. We connect these SHAP structures to microstructure theory (order flow imbalance, spread, and adverse selection) and validate tradability via a conservative top-of-book taker backtest as well as fixed depth maker backtest. Our primary novelty is a robustness analysis of a major flash crash, where the divergent performance of our taker and maker strategies empirically validates classic microstructure theories of adverse selection and highlights the systemic risks of algorithmic trading. Our results suggest a portable microstructure representation of short-horizon returns and motivate universal feature libraries for crypto markets.

2025

• Paweł Sakowski, Rafał Sieradzki, Robert Ślepaczuk (2025), Systemic risk indicator based on implied and realized volatility, Quality & Quantity, Volume 60, Issue 2, Pages 6389-6427

  We propose a new measure of systemic risk to analyze the impact of the major financial market turmoils in the stock markets from 2000 to 2023 in the USA, Europe, Brazil, and Japan. Our Implied Volatility Realized Volatility Systemic Risk Indicator (IVRV_SRI) shows that the reaction of stock markets varies across different geographical locations and the persistence of the shocks depends on the historical volatility and long-term average volatility level in a given market. The methodology applied is based on the logic that the simpler is always better than the more complex if it leads to the same results. Such an approach significantly limits model risk and substantially decreases computational burden. Robustness checks show that IVRV_SRI is a precise and valid measure of the current systemic risk in the stock markets. Moreover, it can be used for other types of assets and high-frequency data. The forecasting ability of various systemic risk indicators (including CATFIN, CISS, Cleveland FED, IVRV_SRI, and SRISK) with regard to weekly returns of S&P 500 index is evaluated based on the simple linear, quasi-quantile, and quantile regressions. We show that IVRV_SRI has the strongest predicting power among them.

• Maciej Wysocki, Robert Ślepaczuk (2025), Systematic index option-writing strategies with Black-Scholes-Merton and Variance-Gamma Models, Economic Modelling, Volume 152, Article 107234

  This study evaluates systematic S&P 500 Index option-writing strategies, comparing the hedging performance of the Black–Scholes-Merton (BSM) and Variance-Gamma (VG) models, bridging the gap between theoretical models and their practical applications in trading. Using 1-minute data from 2018 to 2023, we assess hedged and unhedged strategies against buy-and-hold benchmarks, incorporating transaction costs to validate different hedging and sizing methodologies. Our findings reveal that systematic option writing can generate superior risk-adjusted returns. The BSM model generally outperforms the VG model in hedging, leveraging implied volatility to reflect market conditions accurately. However, the VG model proves valuable for position sizing in certain naked strategies, capturing skewness and kurtosis to manage tail risks. Intraday hedging at 130 min intervals offers effective downside protection while preserving return potential. The insights on hedging and sizing presented in this study provide actionable guidance for institutional and non-institutional participants in options markets.

• Bartosz Bieganowski, Robert Ślepaczuk (2025), Supervised autoencoder MLP for financial time series forecasting, Journal of Big Data, Volume 12, Issue 1, Article 207

  This paper investigates the enhancement of financial time series forecasting with the use of neural networks through supervised autoencoders, aiming to improve investment strategy performance. It specifically examines the impact of noise augmentation and triple barrier labeling on risk-adjusted returns, using the Sharpe and Information Ratios. The study focuses on the S&P 500 index, EUR/USD, and BTC/USD as the traded assets from January 1, 2016, to April 30, 2022. Findings indicate that supervised autoencoders, with balanced noise augmentation and bottleneck size, significantly boost strategy effectiveness. However, excessive noise and large bottleneck sizes can impair performance, highlighting the importance of precise parameter tuning. This paper also presents a derivation of a novel optimization metric that can be used with triple barrier labeling. The results of this study have substantial policy implications, suggesting that financial institutions and regulators could leverage techniques presented to enhance market stability and investor protection, while also encouraging more informed and strategic investment approaches in various financial sectors.

• Maciej Wysocki, Wiktor Budziński, Marek Giergiczny, Robert Ślepaczuk (2025), The cointegration of Polish timber sales channels: Patterns and implications, Forest Policy and Economics, Volume 178, Article 103566

  This study examines the cointegration of timber prices across key sales channels in the Polish timber market, with a focus on competitive dynamics and international integration. Poland’s State Forests National Forest Holding, managing 82% of the country’s forested areas and providing over 95% industrial timber, has a near-monopoly structure. Timber sales are facilitated through three main channels: PL-D, the e-Drewno System, and e-Drewno Individual Auctions. Using cointegration analysis, we assess the connection between these channels and European timber markets. Our findings show limited cointegration in the PL-D and e-Drewno System channels, suggesting they are insulated from international price fluctuations due to restricted access requirements based on purchase history. Conversely, e-Drewno Individual Auctions-open to all without entry restrictions-demonstrate substantial cointegration with other European markets, indicating a higher level of competitiveness and responsiveness to external price trends. Additionally, aggregate prices across all channels exhibit moderate cointegration with international markets, reflecting both price stability and adaptation to broader market trends. These findings reveal structural limitations in the Polish timber market: established firms benefit from stable pricing in restricted channels, while new entrants face higher costs in the more volatile, open channels. Policy implications suggest the need for reforms to enhance market inclusivity and prepare for potential supply constraints under changing environmental and regulatory conditions. This research highlights the critical role of channel-specific structures in shaping market behavior and influencing international integration in the timber industry.

• Damian Ślusarczyk, Robert Ślepaczuk (2025), Optimal Markowitz portfolio using returns forecasted with time series and machine learning models, Journal of Big Data, Volume 12, Issue 1, Article 127

  We aim to answer whether using forecasted stock returns based on machine learning and time series models in a mean-variance portfolio framework yields better results than relying on historical returns. Nevertheless, the problem of efficient stock selection has been tested for more than 50 years, and the issue of adequate construction of a mean-variance portfolio framework and incorporating forecasts of returns has not yet been solved. Stock returns portfolios were created using ‘raw’ historical returns and forecasted returns based on ARIMA-GARCH and the XGBoost models. Two optimization problems were concerned: global maximum information ratio and global minimum variance. Then strategies were compared with two benchmarks—an equally weighted portfolio and buy and hold on the Dow Jones Industrial Average (DJIA) index. Strategies were tested on DJIA stocks in the period from 2007-01-01 to 2022-12-31 and daily data was used. The main portfolio performance metrics were information ratio and modified information ratio. The results showed that by using forecasted returns, we can enhance our portfolio selection based on the Markowitz framework, but it is not a universal solution, and we have to control all the parameters and hyperparameters of selected models. This research paper contributes to the field of Financial Engineering by applying ARIMA-GARCH bootstrapping forecasts and XGBoost forecasts in portfolio optimization and testing a wide range of hyperparameters. Contrary to most similar papers in which a much smaller number of fits are performed, we present an approach that requires fitting tens of models each period, resulting in thousands of fits only in the base case scenario. Such a method requires specific handling and poses new challenges in testing and optimizing the models. Moreover, we are not aware of any other paper that compares the performance of ARIMA-GARCH bootstrapping forecasts and XGBoost forecasts in terms of portfolio optimization.

• Kamil Kashif, Robert Ślepaczuk (2025), LSTM-ARIMA as a hybrid approach in algorithmic investment strategies, Knowledge-Based Systems, Volume 320, Article 113563

  This study focuses on building an algorithmic investment strategy employing a hybrid approach that combines LSTM and ARIMA models referred to as LSTM-ARIMA. This unique algorithm uses LSTM to produce final predictions but boosts the results of this RNN by adding the residuals obtained from ARIMA predictions among other inputs. The combination of LSTM and ARIMA leverages the strengths of both models, with LSTM effectively capturing non-linear patterns in the data, while ARIMA contributes by modeling linear relationships and accounting for autocorrelations, thereby enhancing the overall predictive power and accuracy of the hybrid model. The base LSTM-ARIMA strategy was then compared to RandomForest-ARIMA and Buy&Hold strategy. The algorithm is tested across three equity indices (S&P 500, FTSE 100, and CAC 40) using daily frequency data spanning from January 2000 to August 2023. The architecture of testing is based on the walk-forward procedure which is applied for the hyperparameter tunning phase that uses Random Search and backtesting the algorithms. The selection of the optimal model is determined based on adequately selected performance metrics combining focused on risk-adjusted return measures. We considered two strategies for each algorithm: Long-Only and Long-Short to present the situation of two various groups of investors with different investment policy restrictions. For each strategy and equity index, we compute the performance metrics and visualize the equity curve to identify the best strategy with the highest modified information ratio (( I R ∗ ∗ )). The findings conclude that the LSTM-ARIMA algorithm outperforms all the other algorithms across all the equity indices which confirms the strong potential behind hybrid ML-TS (machine learning - time series) models in searching for the optimal algorithmic investment strategies.

• Sugarbayar Enkhbayar, Robert Ślepaczuk (2025), Predictive modeling of foreign exchange trading signals using machine learning techniques, Expert Systems with Applications, Volume 285, Article 127729

  This study aimed to apply the algorithmic trading strategy on major foreign exchange pairs and compare the performances of machine learning-based and traditional momentum strategies with benchmark strategies. It differs from other studies in that it considered various cases, including different foreign exchange pairs, return methods, data frequency, and individual and integrated trading strategies. Ridge regression, KNN, RF, XGBoost, GBDT, ANN, LSTM, and GRU models were used for the machine learning-based strategy, while the MA cross strategy was employed for the momentum strategy. Backtests were performed on six major pairs from January 1, 2000, to June 30, 2023, and daily and intraday data were used. The Sharpe ratio was considered as a metric used to refer to economic significance and the independent t-test was used to determine statistical significance. The general findings of the study suggested that the currency market has become more efficient. The rise in efficiency is probably caused by the fact that more algorithms are being used in this market, and information spreads much faster. Instead of finding a trading strategy that works well in all major foreign exchange pairs, our study showed that it is possible to find an effective algorithmic trading strategy that generates a more effective trading signal in each specific case. • Extensive test of Machine Learning (ML) models in the exchange currencies market. • The comparison of ML and Momentum-based investment strategies. • Data science approaches were used and combined to create more effective trading strategies. • Indicating the differences between Neural Networks and other ML models. • Considered various investment signals and avoided overfitting problems using Walk-forward approach.

• Oleh Bilyk, Paweł Sakowski, Robert Ślepaczuk (2025), Investing in VIX Futures Based on Rolling GARCH Models Forecasts, in: Między makroekonomią a rynkami finansowymi. Księga jubileuszowa, Wydawnictwa Uniwersytetu Warszawskiego

  Księga jubileuszowa powstała z okazji 70. urodzin Profesora Ryszarda Kokoszczyńskiego – wybitnego naukowca i autorytetu w polskim środowisku ekonomicznym. Zgromadzone w niej artykuły, przygotowane przez przyjaciół, współpracowników i uczniów Profesora

• Stanisław Łaniewski, Robert Ślepaczuk (2025), Evaluating the Chronos Foundation Model for Daily Stock Index Forecasting, Proceedings of the 2025 International Conference on Information Systems Development (ISD)

  This study empirically evaluates the performance of Chronos, a recent foundation model pre-trained on a large corpus of time series data, for the task of daily stock index forecasting. Using a rolling window framework on historical Nasdaq-100 and S&P 500 data from 1995 to early 2025, we compare zero-shot and fine-tuned Chronos variants against a diverse set of established forecasting methods, including statistical benchmarks (AutoARIMA, ETS), standard deep learning models (DeepAR, DLinear, SimpleFeedForward), other Transformer-based architectures (PatchTST), and ensemble approaches. Our results, based on standard forecasting metrics and simulated trading performance, indicate that zero-shot Chronos provides competitive forecasting accuracy. It is statistically comparable to the best traditional methods, but its derived trading performance lags top benchmarks. The fine-tuned Chronos variant statistically underperformed the zero-shot version in forecast accuracy. These findings highlight the potential of foundation models and underlines the significant challenges in effective fine-tuning.

• Zofia Bracha, Jakub Michańków, Paweł Sakowski (2025), Application of Deep Reinforcement Learning to At-the-Money S&P 500 Options Hedging, Working Papers 2025-25, Faculty of Economic Sciences, University of Warsaw

  This paper explores the application of deep Q-learning to hedging at-the-money options on the S&P 500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging decisions without making explicit model assumptions on price dynamics. The agent was trained on historical intraday prices of S&P 500 call options across years 2004 to 2024, using a single time series of six predictor variables: option price, underlying asset price, moneyness, time to maturity, realized volatility, and current hedge position. A walk-forward procedure was applied for training, which lead to nearly 17 years of out-of-sample evaluation. The performance of the deep reinforcement learning (DRL) agent is benchmarked against the Black–Scholes delta hedging strategy over the same time period. We assess both approaches using metrics such as annualized return, volatility, information ratio, and Sharpe ratio. To test models’ adaptability, we performed simulations across varying market conditions and added constraints such as transaction costs and risk-awareness penalties. Our results show that the DRL agent can outperform traditional hedging methods, particularly in volatile or high-cost environments, highlighting its robustness and flexibility in practical trading contexts. While the agent consistently outperforms delta hedging, its performance deteriorates when the risk-awareness parameter is higher. We also observed that the longer the time interval used for volatility estimation, the more stable the results.

• Jędrzej Maskiewicz, Paweł Sakowski (2025), Can Artificial Intelligence Trade the Stock Market?, Working Papers 2025-14, Faculty of Economic Sciences, University of Warsaw

  The paper explores the use of Deep Reinforcement Learning (DRL) in stock market trading, focusing on two algorithms: Double Deep Q-Network (DDQN) and Proximal Policy Optimization (PPO) and compares them with Buy and Hold benchmark. It evaluates these algorithms across three currency pairs, the S&P 500 index and Bitcoin, on the daily data in the period of 2019-2023. The results demonstrate DRL’s effectiveness in trading and its ability to manage risk by strategically avoiding trades in unfavorable conditions, providing a substantial edge over classical approaches, based on supervised learning in terms of risk-adjusted returns.

• Dinggao Liu, Robert Ślepaczuk, Zhenpeng Tang (2025), EXFormer: A Multi-Scale Trend-Aware Transformer with Dynamic Variable Selection for Foreign Exchange Returns Prediction, arXiv preprint arXiv:2512.12727

  Accurately forecasting daily exchange rate returns represents a longstanding challenge in international finance, as the exchange rate returns are driven by a multitude of correlated market factors and exhibit high-frequency fluctuations. This paper proposes EXFormer, a novel Transformer-based architecture specifically designed for forecasting the daily exchange rate returns. We introduce a multi-scale trend-aware self-attention mechanism that employs parallel convolutional branches with differing receptive fields to align observations on the basis of local slopes, preserving long-range dependencies while remaining sensitive to regime shifts. A dynamic variable selector assigns time-varying importance weights to 28 exogenous covariates related to exchange rate returns, providing pre-hoc interpretability. An embedded squeeze-and-excitation block recalibrates channel responses to emphasize informative features and depress noise in the forecasting. Using the daily data for EUR/USD, USD/JPY, and GBP/USD, we conduct out-of-sample evaluations across five different sliding windows. EXFormer consistently outperforms the random walk and other baselines, improving directional accuracy by a statistically significant margin of up to 8.5–22.8%. In nearly one year of trading backtests, the model converts these gains into cumulative returns of 18%, 25%, and 18% for the three pairs, with Sharpe ratios exceeding 1.8. When conservative transaction costs and slippage are accounted for, EXFormer retains cumulative returns of 7%, 19%, and 9%, while other baselines achieve negative. The robustness checks further confirm the model’s superiority under high-volatility and bear-market regimes. EXFormer furnishes both economically valuable forecasts and transparent, time-varying insights into the drivers of exchange rate dynamics for international investors, corporations, and central bank practitioners.

• Anna Perekhodko, Robert Ślepaczuk (2025), Stochastic Volatility Modelling with LSTM Networks: A Hybrid Approach for S&P 500 Index Volatility Forecasting, arXiv preprint arXiv:2512.12250

  Accurate volatility forecasting is essential in banking, investment, and risk management, because expectations about future market movements directly influence current decisions. This study proposes a hybrid modelling framework that integrates a Stochastic Volatility model with a Long Short Term Memory neural network. The SV model improves statistical precision and captures latent volatility dynamics, especially in response to unforeseen events, while the LSTM network enhances the model’s ability to detect complex nonlinear patterns in financial time series. The forecasting is conducted using daily data from the S and P 500 index, covering the period from January 1 1998 to December 31 2024. A rolling window approach is employed to train the model and generate one step ahead volatility forecasts. The performance of the hybrid SV-LSTM model is evaluated through both statistical testing and investment simulations. The results show that the hybrid approach outperforms both the standalone SV and LSTM models and contributes to the development of volatility modelling techniques, providing a foundation for improving risk assessment and strategic investment planning in the context of the S and P 500.

• Jakub Michańków (2025), Forecasting Probability Distributions of Financial Returns with Deep Neural Networks, SSRN Working Paper

  This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student’s t, and skewed Student’s t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student’s t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.

• Dominik Stempień, Robert Ślepaczuk (2025), Hybrid Models for Financial Forecasting: Combining Econometric, Machine Learning, and Deep Learning Models, SSRN Working Paper

  This research systematically develops and evaluates various hybrid modeling approaches by combining traditional econometric models (ARIMA and ARFIMA models) with machine learning and deep learning techniques (SVM, XGBoost, and LSTM models) to forecast financial time series. The empirical analysis is based on two distinct financial assets: the S&P 500 index and Bitcoin. By incorporating over two decades of daily data for the S&P 500 and almost ten years of Bitcoin data, the study provides a comprehensive evaluation of forecasting methodologies across different market conditions and periods of financial distress. Models’ training and hyperparameter tuning procedure is performed using a novel three-fold dynamic cross-validation method. The applicability of applied models is evaluated using both forecast error metrics and trading performance indicators. The obtained findings indicate that the proper construction process of hybrid models plays a crucial role in developing profitable trading strategies, outperforming their individual components and the benchmark Buy&Hold strategy. The most effective hybrid model architecture was achieved by combining the econometric ARIMA model with either SVM or LSTM, under the assumption of a non-additive relationship between the linear and nonlinear components.

• Krzysztof Płachta, Robert Ślepaczuk (2025), Machine Learning for Daily Return Direction Forecasting: A Comparative Study with Explainable AI Insights, SSRN Working Paper

  This study addresses two interrelated objectives. First, we conduct a comparative evaluation of six supervised learning models: Lasso, Random Forest, LightGBM, LSTM, and two feedforward neural networks, for forecasting the next-day direction of SPY returns. Using a long-horizon of 25 years, expanding-window backtesting framework, we generate strictly out-of-sample forecasts and assess model performance based on risk-adjusted metrics, with the Sortino ratio as the primary criterion. Second, to address the opacity of complex machine learning models, we apply a model-agnostic explainable AI approach to the best-performing model. This involves systematically removing individual features and predefined feature groups, followed by full retraining with hyperparameters optimization, to quantify each variable’s contribution to overall performance. The results were mixed. Lasso, LightGBM, and most notably Random Forest – which achieved a Sortino ratio of 0.61, over 30% higher than the benchmark, and exhibited a substantially lower maximum drawdown – outperformed the buy-and-hold strategy. On the other hand, contrary to expectations, all neural network-based models significantly underperformed. In the second part, feature importance analysis for the Random Forest model suggests that signals based on technical indicators, foreign exchange, and commodity prices consistently contributed to improved performance, while certain interest rate and equity index features were detrimental. These findings emphasize the importance of thoughtful model design and feature selection in the development of machine learning strategies for financial forecasting.

2024

• Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk (2024), Mean Absolute Directional Loss as a new loss function for machine learning problems in algorithmic investment strategies, Journal of Computational Science, Volume 81, Article 102375

  This paper investigates the issue of an adequate loss function in the optimization of machine learning models used in the forecasting of financial time series for the purpose of algorithmic investment strategies (AIS) construction. We propose the Mean Absolute Directional Loss (MADL) function, solving important problems of classical forecast error functions in extracting information from forecasts to create efficient buy/sell signals in algorithmic investment strategies. MADL places appropriate emphasis not only on the quality of the point forecast but also on its impact on the rate of achievement by the investment system based on it. The introduction and detailed description of the theoretical properties of this new MADL loss function are our main contributions to the literature. In the empirical part of the study, based on the data from two different asset classes (cryptocurrencies: Bitcoin and commodities: Crude Oil), we show that our new loss function enables us to select better hyperparameters for the LSTM model and obtain more efficient investment strategies, with regard to risk-adjusted return metrics on the out-of-sample data.

• Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk (2024), Hedging Properties of Algorithmic Investment Strategies Using Long Short-Term Memory and Time Series Models for Equity Indices, Proceedings of the 2024 International Conference on Information Systems Development (ISD)

  This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a novel approach to diversification on the level of ensemble algorithmic investment strategies (AIS) built on the prices of these assets. We employ four types of diverse models (LSTM, ARIMA-GARCH, momentum, contrarian) to generate price forecasts, which are used to produce investment signals in single and complex AIS. We verify the diversification potential of different types of investment strategies consisting of various assets classes in hedging ensemble AIS built for equity indices (S&P 500). Our conclusion is that LSTM-based strategies outperform the other models and that the best diversifier for the AIS built for the S&P 500 index is the AIS built for Bitcoin. Finally, we test the LSTM model for 1-hour frequency of data. We conclude that it outperforms the results obtained using daily data.

• Jakub Michańków, Łukasz Kwiatkowski, Janusz Morajda (2024), Combining Deep Learning and GARCH Models for Financial Volatility and Risk Forecasting, Proceedings of the 2024 International Conference on Information Systems Development (ISD)

  In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining econometric GARCH models with deep learning networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used for GARCH: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily returns on the S&P 500 index and Bitcoin prices. As the main volatility estimator, also the target function of our hybrid models, we use the modified Garman-Klass estimator. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets’ risk using the Value-at-Risk (VaR) and Expected Shortfall (ES). Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. It can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior risk forecasts.

• Mateusz Kijewski, Robert Ślepaczuk, Maciej Wysocki (2024), Predicting Prices of S&P 500 Index Using Classical Methods and Recurrent Neural Networks, Proceedings of the 2024 International Conference on Information Systems Development (ISD)

  This study implements algorithmic investment strategies based on classical methods and a recurrent neural network model. The research compares the performance of investment algorithms on time series of the S&P 500 Index covering 20 years of data from 2000 to 2020. We present an approach for the dynamic optimization of parameters during the backtesting process by using a rolling training-testing window. Each method was tested in terms of robustness to changes in parameters and evaluated by appropriate performance statistics, such as the Information Ratio and Maximum Drawdown. The combination of signals from different methods was stable and outperformed the benchmark of the Buy&Hold strategy, doubling its returns while maintaining the same level of risk. Detailed sensitivity analysis revealed that classical methods utilizing a rolling training-testing window were significantly more robust to changes in parameters than the LSTM model.

• Bartosz Bieganowski, Robert Ślepaczuk (2024), Supervised Autoencoders with Fractionally Differentiated Features and Triple Barrier Labelling Enhance Predictions on Noisy Data, arXiv preprint arXiv:2411.12753

  This paper investigates the enhancement of financial time series forecasting with the use of neural networks through supervised autoencoders (SAE), to improve investment strategy performance. Using the Sharpe and Information Ratios, it specifically examines the impact of noise augmentation and triple barrier labeling on risk-adjusted returns. The study focuses on Bitcoin, Litecoin, and Ethereum as the traded assets from January 1, 2016, to April 30, 2022. Findings indicate that supervised autoencoders, with balanced noise augmentation and bottleneck size, significantly boost strategy effectiveness. However, excessive noise and large bottleneck sizes can impair performance.

• Szymon Lis, Robert Ślepaczuk, Paweł Sakowski (2024), Explaining and Forecasting Abnormal Returns and Volume by Investor Sentiment Indicators, Working Papers 2024-18, Faculty of Economic Sciences, University of Warsaw

  This study investigates the impact of investor sentiment on stock returns and trading volume, challenging the efficient market hypothesis. Using CRSP data from May 1998 to March 2022, methods like Fama-MacBeth and quantile regression were applied to analyze sentiment indicators such as the VIX, AAII Investor Sentiment Survey, Consumer Confidence, and Baker-Wurgler Index. The findings reveal that investor sentiment significantly influences stock returns and trading volume, especially during uncertain times. Sentiment also affects financial metrics like SMB, HML, RMW, and CMA uniquely. This research provides new insights and practical implications for investors and analysts, emphasizing the importance of considering sentiment in investment strategies to better anticipate market movements and manage risks.

• Stanisław Łaniewski, Robert Ślepaczuk (2024), Enhancing literature review with NLP methods Algorithmic investment strategies case, Working Papers 2024-16, Faculty of Economic Sciences, University of Warsaw

  This study utilizes machine learning algorithms to analyze and organize knowledge in the field of algorithmic trading, based on filtering 136 million research papers to 14,342 articles ranging from 1956 to Q1 2020. We compare previously used practices such as keyword-based algorithms and embedding techniques with state-of-the-art dimension reduction and clustering for topic modeling method (BERTopic) to compare the popularity and evolution of different approaches and themes. We show new possibilities created by the last iteration of Large Language Models (LLM) like ChatGPT. The analysis reveals that the number of research articles on algorithmic trading is increasing faster than the overall number of papers. The stocks and main indices comprise more than half of all assets considered, but the growing trend in some classes is much stronger (e.g. cryptocurrencies). Machine learning models have become the most popular methods nowadays, but they are often flawed compared to seemingly simpler techniques. The study demonstrates the usefulness of Natural Language Processing in asking intricate questions about analyzed articles, like comparing the efficiency of different models. We demonstrate the efficiency of LLMs in refining datasets. Our research shows that by breaking tasks into smaller ones and adding reasoning steps, we can effectively address complex questions supported by case analyses.

• Maciej Wysocki, Robert Ślepaczuk (2024), Construction and Hedging of Equity Index Options Portfolios, Working Papers 2024-14, Faculty of Economic Sciences, University of Warsaw

  This research presents a comprehensive evaluation of systematic index option-writing strategies, focusing on S&P500 index options. We compare the performance of hedging strategies using the Black-Scholes-Merton (BSM) model and the Variance-Gamma (VG) model, emphasizing varying moneyness levels and different sizing methods based on delta and the VIX Index. The study employs 1-minute data of S&P500 index options and index quotes spanning from 2018 to 2023. The analysis benchmarks hedged strategies against buy-and-hold and naked option-writing strategies, with a focus on risk-adjusted performance metrics including transaction costs. Portfolio delta approximations are derived using implied volatility for the BSM model and market-calibrated parameters for the VG model. Key findings reveal that system atic option-writing strategies can potentially yield superior returns compared to buy-and-hold benchmarks. The BSM model generally provided better hedging outcomes than the VG model, although the VG model showed profitability in certain naked strategies as a tool for position sizing. In terms of rehedging frequency, we found that intraday heding in 130-minute intervals provided both reliable protection against adverse market movements and a satisfactory returns profile.

• Natalia Roszyk, Robert Ślepaczuk (2024), The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models, Working Papers 2024-13, Faculty of Economic Sciences, University of Warsaw

  Predicting the S&P 500 index’s volatility is crucial for investors and financial analysts as it helps in assessing market risk and making informed investment decisions. Volatility represents the level of uncertainty or risk related to the size of changes in a security’s value, making it an essential indicator for financial planning. This study explores four methods to improve the accuracy of volatility forecasts for the S&P 500: the established GARCH model, known for capturing historical volatility patterns; an LSTM network that utilizes past volatility and log returns; a hybrid LSTM-GARCH model that combines the strengths of both approaches; and an advanced version of the hybrid model that also factors in the VIX index to gauge market sentiment. This analysis is based on a daily dataset that includes data for S&P 500 and VIX index, covering the period from January 3, 2000, to December 21, 2023. Through rigorous testing and comparison, we found that machine learning approaches, particularly the hybrid LSTM models, significantly outperform the traditional GARCH model. The inclusion of the VIX index in the hybrid model further enhances its forecasting ability by incorporating real-time market sentiment. The results of this study offer valuable insights for achieving more accurate volatility predictions, enabling better risk management and strategic investment decisions in the volatile environment of the S&P 500.

• Zuzanna Kostecka, Robert Ślepaczuk (2024), Improving Realized LGD approximation: A Novel Framework with XGBoost for handling missing cash-flow data, Working Papers 2024-12, Faculty of Economic Sciences, University of Warsaw

  The scope for the accurate calculation of the Loss Given Default (LGD) parameter is comprehensive in terms of financial data. In this research, we aim to explore methods for improving the approximation of realized LGD in conditions of limited access to the cash-flow data. We enhance the performance of the method which relies on the differences between exposure values (delta outstanding approach) by employing the machine learning (ML) techniques. The research utilizes the data from the mortgage portfolio of one of the European countries and assumes the close resemblance for similar economic contexts. It incorporates non-financial variables and macroeconomic data related to the housing market, improving the accuracy of loss severity approximation. The proposed methodology attempts to mitigate the country-specific (related to the local legal) or portfolio-specific factors in aim to show the general advantage of applying ML techniques, rather than case-specific relation. We developed an XGBoost model that does not rely on cash-flow data yet enhances the accuracy of realized LGD estimation compared to results obtained with the delta outstanding approach. A novel aspect of our work is the detailed exploration of the delta outstanding approach and the methodology for addressing conditions of limited access to cash-flow data through machine learning models.

• Adam Korniejczuk, Robert Ślepaczuk (2024), Statistical arbitrage in multi-pair trading strategy based on graph clustering algorithms in US equities market, Working Papers 2024-09, Faculty of Economic Sciences, University of Warsaw

  The study seeks to develop an effective strategy based on the novel framework of statistical arbitrage based on graph clustering algorithms. Amalgamation of quantitative and machine learning methods, including the Kelly criterion, and an ensemble of machine learning classifiers have been used to improve risk-adjusted returns and increase the immunity to transaction costs over existing approaches. The study seeks to provide an integrated approach to optimal signal detection and risk management. As a part of this approach, innovative ways of optimizing take profit and stop loss functions for daily frequency trading strategies have been proposed and tested. All of the tested approaches outperformed appropriate benchmarks. The best combinations of the techniques and parameters demonstrated significantly better performance metrics than the relevant benchmarks. The results have been obtained under the assumption of realistic transaction costs, but are sensitive to the changes of some key parameters.

• Michał Woźniak, Robert Ślepaczuk, Marcin Chlebuś (2024), Systematic Bagging Model for Market Risk - Cross Pattern Learning Framework for Value at Risk and Expected Shortfall Estimation, SSRN Working Paper

  This paper proposes a new framework, the Systematic Bagging Model (SBM), for estimating market risk through leveraging ensembling and cross-learning approaches. The SBM is designed to make possible the generation of stable and accurate forecasts for Value at Risk and Expected Shortfall by using deterministic learning sets from time series data with optimal pattern searching. Empirical validation with the LIGHT Benchmark shows the superiority of an SBM over state-of-the-art single models concerning forecasting quality in terms of adequacy, regulatory compliance, and capital effectiveness. This research unveils a strong potential for systematic bagging and cross-learning for improving market risk models, especially during periods of sudden increased volatility.

2023

• Jan Grudniewicz, Robert Ślepaczuk (2023), Application of machine learning in algorithmic investment strategies on global stock markets, Research in International Business and Finance, Volume 66, Article 102052

  The research undertakes the subject of machine learning based algorithmic investment strategies. Several technical analysis indicators were employed as inputs to machine learning models such as Neural Networks, K Nearest Neighbor, Regression Trees, Random Forests, Naïve Bayes classifiers, Bayesian Generalized Linear Models, and Support Vector Machines. Models were used to generate trading signals on WIG20, DAX, S&P500, and selected CEE indices in the period between 2002-01-01 and 2023-03-31. Strategies were compared with each other and with the benchmark buy-and-hold strategy in terms of achieved levels of risk and return. Sensitivity analysis was used to assess the quality of the estimation on independent subsets. The findings of the study showed that algorithmic strategies outperformed passive strategies in terms of risk-adjusted returns and that for the analyzed indices, Linear Support Vector Machine and Bayesian Generalized Linear Model were the best-performing models. The Linear Support Vector Machine was chosen as the model that, on average, produced the best results using a more thorough rank approach based on the outcomes for all examined models and indices.

• Michał Woźniak, Maciej Wysocki, Szymon Lis, Mateusz Kijewski (2023), The Influence of Macro- and Socio-Economic Factors on the Consumption of Music throughout the Year, Metody Ilościowe w Badaniach Ekonomicznych, Volume 24, Issue 1, Pages 1-26

  Popular research methods in assessing the impact of macroeconomic and environmental variables on music preferences were psychological experiments and surveys with small groups or analyzing the effect of one or two variables in the whole population. Instead inspired by the article of The Economist about February being the gloomiest month in terms of music listened to, we have created a dataset with many variables. We used Spotify API to create a dataset with average valence for 26 countries for the period from January 1, 2018, to December 1, 2019. Then we applied the regression and machine learning models to them. Our study confirmed the effects of summer, December, and the number of Saturdays in a month and contradicted the February effect. The influence of GDP per capita on the valence was confirmed, while the impact of the happiness index was disproved. All models partially confirmed the influence of the music genre on the valence. Among the weather variables, two models confirmed the significance of the temperature variable. Macroeconomic variables turned out to have non-linear relationships that made interpretations difficult, while the environmental ones clearly indicated a linear relationship with valence.

• Iskandar Sheraliev, Robert Ślepaczuk (2023), Cross-Country Differences in Return and Volatility Metrics of World Equity Indices, Central European Economic Journal, Volume 10, Pages 90-115

  This research seeks to determine whether the cross-country differences in return and volatility metrics in various country equity indices can be explained by differences in economic development. We base the study on the MSCI IMI net income indices on two samples: a 51-country sample from the period 31 May 2002 to 28 February 2022, and a 75-country sample from the period 30 November 2010 to 28 February 2022. In this study, countries are grouped into four categories: frontier, emerging, early-developed, and developed, based on gross domestic product (GDP) per capita. The Kruskal–Wallis rank sum test is used to find cross-group differences, and the results are further analyzed with the pairwise Wilcoxon rank sum test with the Holm–Bonferroni p value adjustment method. The results are relatively unintuitive and show that there is no significant cross-group difference in daily and monthly returns. There is evidence of a considerable difference in volatility metrics, especially in the case of the emerging market group, which is significantly different from the three other groups. The results are slightly sensitive to time period change and very sensitive to changes in income categories of some countries.

• Małgorzata Jabłczyńska, Krzysztof Kość, Przemysław Ryś, Paweł Sakowski, Robert Ślepaczuk, Grzegorz Zakrzewski (2023), Energy and cost efficiency of Bitcoin mining endeavor, PLOS ONE, Volume 18, Issue 3, Article e0283687

  The main aim of the study is to analyze BTC mining’s efficiency under current market conditions (December 2021), including soaring energy prices produced from many different sources in different geographical locations. After a thorough analysis of initial assumptions concerning the (1) price of mining machine with associated components and its effective amortization period, (2) difficulty and the hash rate of the BTC network, (3) BTC transaction fees, and (4) energy costs from various sources, we have found that currently, BTC mining is not profitable, except for some rare cases. The main reason for this phenomenon is the fast and unpredictable increase of difficulty of the BTC network over time which results in decreasing participation of already purchased mining machines in the BTC network hash rate. The research is augmented with a detailed sensitivity analysis of mining efficiency to initial parameters assumptions, which allows observing that the conditions for BTC mining to be efficient and profitable are very challenging.

• Sahil Teymurzade, Robert Ślepaczuk (2023), Predicting DJIA, NASDAQ and NYSE index prices using ARIMA and VAR models, Working Papers 2023-27, Faculty of Economic Sciences, University of Warsaw

  This paper implements automated trading strategies with buy/sell signals based on Autoregressive Integrated Moving Average (ARIMA) and Vector autoregression (VAR) models. ARIMA and VAR models are compared based on several forecast error measures and investment performance statistics. The data used in this thesis are daily closing prices of Dow Jones Industrial Average, NASDAQ Composite and NYSE Composite indices. The trading period covers 20 years of data from 2000-11-30 to 2020-11-30. The sensitivity analysis is made by changing the initial parameters to test how robust the methods are to these changes. Results show that although ARIMA model performed remarkably well during the volatile periods, VAR based strategy had better investment performance and was less robust to the changes compared to the ARIMA based strategy. Additionally, we have found that error metrics might be insufficient to evaluate performance of forecasting models, as VAR with higher forecast errors outperformed ARIMA model in algorithmic trading strategies.

• Paweł Jakubowski, Robert Ślepaczuk, Franciszek Windorbski (2023), Ensembling ARIMAX Model in Algorithmic Investment Strategies on Commodities Market, Working Papers 2023-20, Faculty of Economic Sciences, University of Warsaw

  This paper presents the results of investment strategies based on predictions from an ARIMA with exogenous variables (ARIMAX/ARIMAX-Garch) model, using the prices of selected commodities and companies from the DJIA index as explanatory variables. The explained variables are four Invesco ETF funds (DBE, DBA, DBP, DBB) corresponding to baskets of energy, agricultural, precious, and industrial metals. The models are optimized using the Walk-Forward technique, and the selection of exogenous variables is based on Granger causality tests. By analyzing the results, we conclude that ARIMAX/ARIMAX-Garch models are not useful tools for making buy or sell decisions for the selected commodity baskets. Out of the 80 estimated models, 44 outperform the Buy & Hold strategy, however, none achieved statistically significant results. Combining individual models into an investment portfolio reduced the risk without significantly reducing the profit, enabling us to consistently beat the benchmark. We also observe that using returns of commodities listed on stock exchanges is more effective than using stock returns. Sensitivity analysis shows instability in results with changes in the length of the training and testing windows. The highest annual return rate of 15.37% from 02.01.2008 to 01.12.2022 was characterized by an ARIMAX model with one commodity exogenous variable.

• Karol Chojnacki, Robert Ślepaczuk (2023), Ensembled LSTM with Walk Forward Optimization in Algorithmic Trading, Working Papers 2023-15, Faculty of Economic Sciences, University of Warsaw

  This study compares well-known tools of technical analysis (Moving Average Crossover MAC) with Machine Learning based strategies (LSTM and XGBoost) and Ensembled Machine Learning Strategies (LSTM ensembled with XGBoost and MAC). All models were compared to Buy and Hold benchmark and evaluated using Performance Metrics, that is Annualized Return Compounded, Maximum Drawdown, Maximum Loss Duration, and three types of Information Ratio. This research uses daily S&P 500 index data ranging from 2000 to 2023. Every strategy was optimized with novel walk forward approach consisting of numerous in sample and out of sample periods. MAC and best performing ML methods were subjected to sensitivity analysis. The results show that LSTM ensembled with XGBoost and MAC yields the most promising results in terms of risk-adjusted returns which suggest further research focused on ensembling of individual ML strategies. Finally, we show that classical methods of technical analysis (that is, MAC) are much less robust and indifferent to change in hyperparameters than machine learning based algorithms, especially LSTM

• Maudud Hassan Uzzal, Robert Ślepaczuk (2023), The performance of time series forecasting based on classical and machine learning methods for S&P 500 index, Working Papers 2023-05, Faculty of Economic Sciences, University of Warsaw

  Based on one step ahead forecasts, this study compares the forecasting abilities of the traditional technique (ARIMA) with recurrent neural network (LSTM). In order to check the possible use of these forecasts in different asset management methods, these forecasts are afterwards included into trading signals of investment strategies. As a benchmark method, the Random Walk model producing naive forecasts has been utilized. This research examines daily data from the S&P 500 index for 20 years, from 2000 to 2020, and it includes information on some significant market turbulence. The methods were tested in terms of robustness to changes in parameters and hyperparameters and evaluated based on various error metrics (MAE, MAPE, RMSE MSE). The results show that ARIMA outperforms LSTM in terms of one step ahead forecasts. Finally, LSTM model with a variety of hyperparameters - including a number of epochs, a loss function, an optimizer, activation functions, a number of units, a batch size, and a learning rate - was tested in order to check its robustness.

• Michał Woźniak, Robert Ślepaczuk (2023), LIGHT Benchmark - Comprehensive Backtesting Framework for Market Risk Models Comparison, SSRN Working Paper

  The aim of the article is to present LIGHT Benchmark - a real world, multidimensional, comprehensive, and agnostic backtesting framework for market risk models comparison. The algorithm allows for reliable assessment of the quality of the classic and state of the art Value at Risk and Expected Shortfall models in the form of a scoreboard. Our benchmark consists of 375 validation paths, of which two thirds are dedicated to Value at Risk and one third to Expected Shortfall. Each proposed scenario is independent and meets the requirements of the median research on market risk estimation, i.e., meeting the capital requirements imposed by the regulator and optimising day-to-day operations in terms of the amount of reserves held. Taking it into account, we cover following categories of validation techniques during the scoring procedure: fulfilling regulatory requirements, forecasting adequateness and capital effectiveness. Benchmark paths are built on such dimensions as: asset categories, representatives of each asset category, testing periods, testing period sizes, testing horizons and VaR and ES confidence levels. Our scenarios are built based on our own calculations and an extensive quantitative literature review. In addition, we propose our expert scoring system, which is designed to aggregate individual scores into a final scoreboard. This system has been tested for stability and compatibility with other popular methods such as Model Confidence Set Procedure. The data used in this benchmark has a daily frequency and comes from the period from 2000 to 2021. Additionally, to present LIGHT Benchmark in practice we utilise it to score classic but also the most promising econometric models for the problem of market risk.

2022

• Quynh Bui, Robert Ślepaczuk (2022), Applying Hurst Exponent in pair trading strategies on Nasdaq 100 index, Physica A: Statistical Mechanics and its Applications, Volume 592, Article 126784

  This research aims to seek an alternative approach to pair selection for the purpose of pair trading strategy. We try to build an effective pair trading strategy based on 103 stocks listed in NASDAQ-100 index. The dataset has daily frequency and covers the period from 01/01/2000 to 31/12/2018. In this study, Generalized Hurst Exponent, Correlation and Cointegration are employed to detect the mean-reverting pattern in the time series of linear combination of each pair of stock. The result show that Hurst method cannot outperform the benchmark, which implies that market is efficient. This result is quite sensitive to varying number of pairs traded and rebalancing period and less sensitive to financial leverage degree. Moreover, Hurst method is better than cointegration method but is not superior as compared to correlation method.

• Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk (2022), LSTM in Algorithmic Investment Strategies on BTC and S&P500 Index, Sensors, Volume 22, Issue 3, Article 917

  We use LSTM networks to forecast the value of the BTC and S&P500 index, using data from 2013 to the end of 2020, with the following frequencies: daily, 1 h, and 15 min data. We introduce our innovative loss function, which improves the usefulness of the forecasting ability of the LSTM model in algorithmic investment strategies. Based on the forecasts from the LSTM model we generate buy and sell investment signals, employ them in algorithmic investment strategies and create equity lines for our investment. For this purpose we use various combinations of LSTM models, optimized on in-sample period and tested on out-of-sample period, using rolling window approach. We pay special attention to data preprocessing in the input layer, to avoid overfitting in the estimation and optimization process, and assure correct selection of hyperparameters at the beginning of our tests. The next stage is devoted to the conjunction of signals from various frequencies into one ensemble model, and the selection of best combinations for the out-of-sample period, through optimization of the given criterion in a similar way as in the portfolio analysis. Finally, we perform a sensitivity analysis of the main parameters and hyperparameters of the model.

• Nguyen Vo, Robert Ślepaczuk (2022), Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index, Entropy, Volume 24, Issue 2, Article 158

  This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data collected from Yahoo Finance with daily frequency for the period from 1 January 2000 to 31 December 2019. By using a rolling window approach, we compared ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than the simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we compared their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE), and their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio, and adjusted information ratio). The main contribution of this research is to show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index) over the long term. These results are not sensitive to varying window sizes, the type of distribution, and the type of the GARCH model.

• Thi Huyen Tran, Robert Ślepaczuk (2022), Quantile regression analysis to predict GDP distribution using data from the US and UK, Working Papers 2022-30, Faculty of Economic Sciences, University of Warsaw

  This paper aims to find the best models to forecast one-quarter-ahead and one-year-ahead US and UK real GDP growth distributions by employing quantile regression with skewed-t distribution on different sets of relevant near-term predictors. The research data period starts in 1947Q1/1955Q1 for US/UK data and ends in 2021Q3/2020Q4 for one-quarter-ahead/one-year-ahead prediction. The out-of-sample period ranges from 1996Q3 to 2021Q3 for one-quarter-ahead prediction and to 2020Q4 for one-year-ahead forecasting. The author applies a two-step testing procedure, in which models with the lowest average error in out-of-sample period are selected to the next step where the cumulative distribution functions of probability integral transforms are computed for the out-of-sample period, to select the best models. The improvement in the final forecasts of the tested models results, among others, from the use of new macroeconomic data with a higher frequency and focusing on the specific properties of the tested models separately for the US and UK. The chosen best models indicate that there exist better models than the model proposed by Adrian et al. (2016) to predict US growth distributions and that near-term predictors can produce good UK growth forecasts. Additionally, some simplified models associated with significantly lower portion of model risk are detected to produce meaningful forecasts for both US and UK case. For the US data, there exist several models that can produce timely predicted results.

• Thi Thu Giang Nguyen, Robert Ślepaczuk (2022), The efficiency of various types of input layers of LSTM model in investment strategies on S&P500 index, Working Papers 2022-29, Faculty of Economic Sciences, University of Warsaw

  The study compares the use of various Long Short-Term Memory (LSTM) variants to conventional technical indicators for trading the S&P 500 index between 2011 and 2022. Two methods were used to test each strategy: a fixed training data set from 2001–2010 and a rolling train–test window. Due to the input sensitivity of LSTM models, we concentrated on data processing and hyperparameter tuning to find the best model. Instead of using the traditional MSE function, we used the Mean Absolute Directional Loss (MADL) function based on recent research to enhance model performance. The models were assessed using the Information Ratio and the Modified Information Ratio, which considers the maximum drawdown and the sign of the annualized return compounded (ARC). LSTM models’ performance was compared to benchmark strategies using the SMA, MACD, RSI, and Buy&Hold strategies. We rejected the hypothesis that algorithmic investment strategy using signals from LSTM model consisting only from daily returns in its input layer is more efficient. However, we could not reject the hypothesis that signals generated by LSTM model combining daily returns and technical indicators in its input layer are more efficient. The LSTM Extended model that combined daily returns with MACD and RSI in the input layer generated a better result than Buy&Hold and other strategies using a single technical indicator. The results of the sensitivity analysis show how sensitive this model is to inputs like sequence length, batch size, technical indicators, and the length of the rolling train - test window.

• Katarzyna Kryńska, Robert Ślepaczuk (2022), Daily and intraday application of various architectures of the LSTM model in algorithmic investment strategies on Bitcoin and the S&P 500 Index, Working Papers 2022-25, Faculty of Economic Sciences, University of Warsaw

  This thesis investigates the use of various architectures of the LSTM model in algorithmic investment strategies. LSTM models are used to generate buy/sell signals, with previous levels of Bitcoin price and the S&P 500 Index value as inputs. Four approaches are tested: two are regression problems (price level prediction) and the other two are classification problems (prediction of price direction). All approaches are applied to daily, hourly, and 15-minute data and are using a walk-forward optimization procedure. The out-of-sample period for the S&P 500 Index is from February 6, 2014 to November 27, 2020, and for Bitcoin it is from January 15, 2014 to December 1, 2020. We discover that classification techniques beat regression methods on average, but we cannot determine if intra-day models outperform inter-day models. We come to the conclusion that the ensembling of models does not always have a positive impact on performance. Finally, a sensitivity analysis is performed to determine how changes in the main hyperparameters of the LSTM model affect strategy performance.

• Illia Baranochnikov, Robert Ślepaczuk (2022), A comparison of LSTM and GRU architectures with novel walk-forward approach to algorithmic investment strategy, Working Papers 2022-21, Faculty of Economic Sciences, University of Warsaw

  The aim of this work is to build a profitable algorithmic investment strategy on various types of assets. The algorithm is built using recurrent neural networks (LSTM and GRU) as the primary source of signals to buy/sell financial instruments. LSTM and GRU architectures are compared in terms of obtaining the best results and beating the market. The algorithm is tested for four financial instruments (Bitcoin, Tesla, Brent Oil and Gold) on daily and hourly data frequencies. The out-of-sample period is from 1 January 2021 to 1 April 2022. A walk-forward process is responsible for training models and selecting the best model to forecast asset prices in the future. Ten model architectures with various hyperparameters are trained during each step of the walk-forward process. The model architecture with the highest Information Ratio (IR*) in the validation period is used for forecasting in the out-of-sample period. For each strategy, the performance metrics are calculated based on which the profitability of the algorithm is evaluated. At the end, a detailed sensitivity analysis with regards to the main hyperparameters is conducted. The results reveal that LSTM outperforms GRU in most of the cases and that investment strategy built based on LSTM/GRU architecture is able to beat the market only on 50% of tested cases.

• Maciej Wysocki, Paweł Sakowski (2022), Investment Portfolio Optimization Based on Modern Portfolio Theory and Deep Learning Models, Working Papers 2022-12, Faculty of Economic Sciences, University of Warsaw

  This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. In this study we propose a novel framework for variance-covariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the long short-term memory (LSTM) recurrent neural networks (RNN) along with two probabilistic deep learning models: DeepVAR and GPVAR to the task of one-day ahead multivariate forecasting. We then use these forecasts to optimize portfolios that consisted of stocks and cryptocurrencies. Our analysis presents results across different combinations of observation windows and rebalancing periods to compare performances of classical and deep learning variance-covariance estimation methods. The conclusions of the study are that although the strategies (portfolios) performance differed significantly between different combinations of parameters, generally the best results in terms of the information ratio and annualized returns are obtained using the LSTM-RNN models. Moreover, longer observation windows translate into better performance of the deep learning models indicating that these methods require longer windows to be able to efficiently capture the long-term dependencies of the variance-covariance matrix structure. Strategies with less frequent rebalancing typically perform better than these with the shortest rebalancing windows across all considered methods.

• Baiquan Ma, Robert Ślepaczuk (2022), The profitability of pairs trading strategies on Hong-Kong stock market: distance, cointegration, and correlation methods, Working Papers 2022-02, Faculty of Economic Sciences, University of Warsaw

  This research aims to compare the profitability of correlation-based pair trading strategy, cointegration-based pair trading strategy, and distance-based pair trading strategy on the Hong Kong stock market. We try to build an effective pair trading strategy based on 50 stocks listed in the Hang Seng index joining them in market-neutral pairs. The dataset has a daily frequency and covers the period from 07/01/2013 to 07/01/2020. The result shows that all three methods are profitable in the Hong Kong stock market and can beat the market with regard to risk-adjusted return metrics. This result is quite sensitive to the varying number of pairs traded and rebalancing period and less sensitive to financial leverage degree. Moreover, the cointegration method is superior as compared to the correlation method and distance method.

2021

• Maciej Wysocki, Robert Ślepaczuk (2021), Artificial Neural Networks Performance in WIG20 Index Options Pricing, Entropy, Volume 24, Issue 1, Article 35

  In this paper, the performance of artificial neural networks in option pricing was analyzed and compared with the results obtained from the Black–Scholes–Merton model, based on the historical volatility. The results were compared based on various error metrics calculated separately between three moneyness ratios. The market data-driven approach was taken to train and test the neural network on the real-world options data from 2009 to 2019, quoted on the Warsaw Stock Exchange. The artificial neural network did not provide more accurate option prices, even though its hyperparameters were properly tuned. The Black–Scholes–Merton model turned out to be more precise and robust to various market conditions. In addition, the bias of the forecasts obtained from the neural network differed significantly between moneyness states. This study provides an initial insight into the application of deep learning methods to pricing options in emerging markets with low liquidity and high volatility.

• Jakub Michańków (2021), Forecasting accuracy evaluation of deep recurrent networks, in: Knowledge, Economy, Society: Business Development in Digital Economy and COVID-19 Crisis, Cracow University of Economics

  The main goal of this paper is to assess and evaluate forecasting accuracy of selected recurrent deep neural networks, based on the hypothesis that these types of networks can be successfully used to provide point forecasts of stock returns. The focus is on model prediction accuracy when working with financial time series data, mainly logarithmic stock market returns. Several types of deep recurrent networks are tested, with an emphasis on recurrent neural networks (RNN), long short-term memory networks (LSTM) and gated recurrent unit (GRU) networks.

• Jakub Michańków (2021), Modelling univariate time series with one-dimensional convolutional neural networks, in: The Book of Articles, National Scientific Conference “Knowledge – Key to Success”, V edition

  The goal of this article is to present theoretical concepts and applications of one-dimensional convolutional neural networks in univariate time series data modeling and prediction. While highly popular, CNNs are mostly used for working with two-dimensional image data. This work shows that they can also be successfully applied for modeling time series data. The methodology used in this research is computer simulation. A model based on one-dimensional convolutional network is programmed to train on two different time series data sets – daily temperature data and Tesla stock prices. Root-mean-square error (RMSE) and mean absolute percentage error (MAPE) measures were used to evaluate model performance. In both cases, the model performs quite well, although the results obtained on the stock prices data are slightly better. The work also indicates the possibilities of improving and streamlining the models based on the described methods.

• Sergio Castellano Gómez, Robert Ślepaczuk (2021), Robust optimisation in algorithmic investment strategies, Working Papers 2021-27, Faculty of Economic Sciences, University of Warsaw

  This research develops a portfolio of four algorithmic strategies that produce Long/Short signals based on t+1 close price predictions of the underlying instrument. The main instrument used is S&P 500 index, and the data covers the period from 1990-01-01 to 2021-04-23. Each strategy is based on a different theory and aims to perform well in different market regimes. The objective is to have a set of uncorrelated investment strategies based on different logics such as trend-following, contrarian approach, statistical methods, and macro-economic news. Each strategy was individually generated following a personalized Walk-Forward optimisation, in which the model seeks to choose the most robust combination of parameters rather than the best one, in terms of risk-adjusted returns. The robustness of all strategies was tested by changing all parameters selected at the beginning of the optimisation. Additionally, the robustness of the portfolio of strategies is tested by applying it to another American index, Nasdaq Composite. Finally, the ensemble model was created based on the combination of the signals from all investment strategies for our two basis instruments. Results show that the portfolio obtains returns four (seven) times larger than the Buy & Hold strategy on S&P 500 (Nasdaq Composite) with a similar level of risk in the last 31 years.

• Kamil Korzeń, Robert Ślepaczuk (2021), Enhanced Index Replication Based on Smart Beta and Tail-Risk Asset Allocation, Working Papers 2021-18, Faculty of Economic Sciences, University of Warsaw

  The following research paper’s main goal is to create an algorithmically managed ETF, which tracks the SPX index and provides a Smart Beta exposure. Authors apply the following simple index replication methods: partial correlation, non-negative least squares, beta coefficient, and dynamic time warping. First, authors are trying to reverse engineer the Index Tracking process in an automated and fair manner - taking into account e.g. transaction costs. Additionally, authors apply a constraint to the total number of assets used in the replication process, which is limited to the certain N. Then, authors develop a Smart Beta framework based on limiting the negative tail-risk. The positive excess return (alpha) is captured and used to compensate for the underperformance of the replicated Index or paid in a form of a dividend. Moreover, with the enhancement methods applied (Kurtosis/Skewness and Excess Return Cushion (ERC) enhancements), the authors’ main goal is to keep the Tracking Error (TE) on a fixed level, although with a significant overweight on the Positive TE and underweight on the Negative TE. In the research paper, the data from 04-Jan-2016 to 31-Dec-2020 is used as the training window, while the first quarter of the year 2021 (Q1 2021) is used as an out-of-sample and out-of-time testing period. Additionally, the authors measure the replicated Index’s performance compared to the SPY, VOO, and IVV ETFs. Authors find a piece of empirical evidence that it is possible to track the SPX Index within the limits of 4-5% TE with the limited number of assets. Moreover, after the implementation of alpha accumulation, the authors outperform the benchmark ETFs in terms of minimizing the TE but did not succeed in providing statistically significant returns better than the SPX Index.

• Mateusz Kijewski, Szymon Lis, Michał Woźniak, Maciej Wysocki (2021), Don’t Worry, Be Happy – But Only Seasonally, Working Papers 2021-12, Faculty of Economic Sciences, University of Warsaw

  Current scientific knowledge allows us to assess the impact of socioeconomic variables on musical preferences. The research methods in these studies were psychological experiments and surveys conducted on small groups or analyzing the influence of only one or two variables at the level of the whole society. Instead inspired by the article of The Economist about February being the gloomiest month in terms of music listened to, we have created a dataset with many different variables that will allow us to create more reliable models than the previous datasets. We used the Spotify API to create a monthly dataset with average valence for 26 countries for the period from January 1, 2018, to December 1, 2019. Our study almost fully confirmed the effects of summer, December, and number of Saturdays in a month and contradicted the February effect. In the context of the index of freedom and diversity, the models do not show much consistency. The influence of GDP per capita on the valence was confirmed, while the impact of the happiness index was disproved. All models partially confirmed the influence of the music genre on the valence. Among the weather variables, two models confirmed the significance of the temperature variable. All in all, effects analyzed by us can broaden artists’ knowledge of when to release new songs or support recommendation engines for streaming services.

2020

• Michał Latoszek, Robert Ślepaczuk (2020), Does the Inclusion of Exposure to Volatility into Diversified Portfolio Improve the Investment Results? Portfolio Construction from the Perspective of a Polish Investor, Economics and Business Review, Volume 6(20), Issue 1, Pages 46-81

  The main goal of this research is to analyse the investment benefits from an incorporation of the volatility exposure to the diversified portfolio from the perspective of a Polish investor. Volatility, treated as a new asset class, may improve the performance of the portfolio due to its negative correlation with most types of assets. This topic has been widely investigated for the United States and Europe whereas the Polish market appears to be not heavily researched and this study may fill this gap. The research covers the period from October 2010 to July 2018 and is performed on daily close prices. To construct the portfolios the analysis uses the mean-variance framework and the naïve diversification approach. The comparison of risk-adjusted returns between investments with and without volatility exposure enables an answer to the research question about an improvement of the results by the addition of a non-standard asset to the diversified portfolios. The VXX is considered as the proxy for volatility as it is the most popular ETN which follows the volatility index derivatives with the given maturity. To test the robustness of the results the portfolios are constructed with a broad range of different parameters and assumptions imposed on the optimization procedure.

• Paweł Sakowski, Daria Turovtseva (2020), Does Bitcoin Improve Investment Portfolio Efficiency?, Working Papers 2020-42, Faculty of Economic Sciences, University of Warsaw

  The aim of the paper is to check if cryptocurrency Bitcoin – a new investable asset class representative – is able to improve the performance of an optimal portfolio. Using two Markowitz criteria of optimization – expected return maximization and expected shortfall (CVaR) minimization – we test the investment opportunities after adding Bitcoin to the portfolio of 10 traditional assets (among them equity, fixed income, money, commodities and money market indices). Using daily observations from 1.05.2013 till 24.05.2019, we examine the behavior of the portfolios without and with Bitcoin and check if the return-risk ratio improves for the latter. Discussing the results, we conduct the sensitivity analysis by changing the lookback window (LB) and rebalancing frequency (RB) parameters. Empirical analysis suggests that Bitcoin-inclusive portfolios provide an investor with wider diversification opportunities. Robustness check confirms the findings and also advocates for the cryptocurrency to be added to the portfolio.

• Paweł Sakowski, Anna Turovtseva (2020), Verification of Investment Opportunities on the Cryptocurrency Market within the Markowitz Framework, Working Papers 2020-41, Faculty of Economic Sciences, University of Warsaw

  The aim of the paper is to reveal if the classical approach for asset allocation can be reflected on an innovative market of cryptocurrencies. Markowitz rebalanced portfolio technique is employed for this purpose. The filtering of coins for optimization is done on the whole scope of cryptocurrencies available for the time horizon of the study and only 52 coins get into the portfolio at least once. There are four primary strategies produced within a set of assumed optimization parameters together with four benchmarks for each. The benchmarks are Bitcoin buy-and-hold, S&P500 buy-and-hold, equally weighted portfolio and portfolio weighted by market capitalization. While looking at the performance measures, it is concluded that Markowitz strategies outperform their benchmarks for every set of parameters. The results of the sensitivity analysis suggest that there is a big potential in finding profitable strategy of investment on cryptocurrencies. The change of parameters: look-back period, rebalancing window, transaction cost as well as optimization objective impact the strategies performance significantly. Eventually, there appear a strategy in the sensitivity analysis, which performs better than the primary ones due to the prolonged parameters of look-back period and rebalancing window.

• Robert Ślepaczuk, Igor Wabik (2020), The impact of the results of football matches on the stock prices of soccer clubs, Working Papers 2020-35, Faculty of Economic Sciences, University of Warsaw

  The aim of this paper is to study the relationship between sport results and stock prices of European football clubs. To show that connection, we use two econometric models. Firstly, we conduct an event study analysis around the dates of football games to look for existence of abnormal returns. Secondly, we use OLS regression to test what effect the unexpected part of the result has. Based on 2239 observations of football matches results played between 01/08/2016 and 02/03/2020, we find significant relationship between sport results and financial performance. Significant negative abnormal returns are observed around defeats and draws, while for wins the impact is unclear. Using second model, we find positive values for coefficients related to unexpected number of points, which can be an additional evidence of a link between football results and stock prices. Finally, we see the potential for systematic trading strategy on soccer stocks based on the presented results. Such algo strategy with market neutral characteristic should beat the market regardless of market conditions.

• Bartłomiej Bollin, Robert Ślepaczuk (2020), Variance Gamma Model in Hedging Vanilla and Exotic Options, Working Papers 2020-31, Faculty of Economic Sciences, University of Warsaw

  The aim of this research is to explore the performance of different option pricing models in hedging the exotic options using the FX data. We analyze the narrow class of Lévy processes - the Variance Gamma process in hedging vanilla, Asian and lookback options. We pose a question of whether or not using additional level of complexity, by introducing more sophisticated models, improves the effectiveness of hedging options, assuming that hedging errors are measured as the differences between portfolio values according to the model and not real market data (which we don’t have). We compare this model with its special case and the Black-Scholes model. We use the data for EURUSD currency pair assuming that option prices change according to the model (as we don’t observe them directly). We use Monte Carlo methods in fitting the model’s parameters. Our results are not in line with the previous literature as there are no signs of the Variance Gamma process being better than the Black-Scholes and it seems that all three models perform equally well.

• Karol Kielak, Robert Ślepaczuk (2020), Value-at-risk — the comparison of state-of-the-art models on various assets, Working Papers 2020-28, Faculty of Economic Sciences, University of Warsaw

  This paper compares different approaches to Value-at-Risk measurement based on parametric and non-parametric approaches. Three portfolios are taken into consideration — the first one containing only stocks from the London Stock Exchange, the second one based on different assets of various origins and the third one consisting of cryptocurrencies. Data used cover the period of more than 20y. In the empirical part of the study, parametric methods based on mean-variance framework are compared with GARCH(1,1) and EGARCH(1,1) models. Different assumptions concerning returns’ distribution are taken into consideration. Adjustment for the fat tails effect is made by using Student t distribution in the analysis. One-day-ahead 95%VaR estimation is then calculated. Thereafter, models are validated using Kupiec and Christoffersen tests and Monte Carlo Simulation for reliable verification of the hypotheses. The overall goal of this paper is to establish if analyzed models accurately estimate Value-at-Risk measure, especially if we take into account assets with various returns distribution characteristics.

2019

• Kamil Korzeń, Robert Ślepaczuk (2019), Hybrid Investment Strategy Based on Momentum and Macroeconomic Approach, Working Papers 2019-17, Faculty of Economic Sciences, University of Warsaw

  The purpose of this research is to test the potential returns and robustness of an automated investment strategy. The strategy is based on momentum and macroeconomic approach, that consists of the technical core – momentum, and the additional macro screening, which is used to determine whether investment signals generate relevant investment opportunities or just technical noise. In order to check whether the macroeconomic factor is the value added to the momentum strategy, the hybrid approach is tested and compared with the simple momentum and the macroeconomic strategy alone and then assessed on a risk-adjusted return basis. The main aim of this paper is to answer the question, whether an investor can gain surplus risk-adjusted returns from merging short-term momentum strategy with the long-term macroeconomic approach. Strategies are based on the data for the selected companies from the S&P500 index in the period ranging from 02/01/1990 to 31/12/2018.

• Krzysztof Kosc, Paweł Sakowski, Robert Ślepaczuk (2019), Momentum and contrarian effects on the cryptocurrency market, Physica A: Statistical Mechanics and its Applications, Volume 523, Pages 691-701

  We report the results of investigation of the momentum and contrarian effects on cryptocurrency markets. The investigated investment strategies involve 100 (amongst over 1200 present as of date Nov 2017) cryptocurrencies with the largest market cap and average 14-day daily volume exceeding a given threshold value. Investment portfolios are constructed using different assumptions regarding the portfolio reallocation period, width of the ranking window, the number of cryptocurrencies in the portfolio, and the percent transaction costs. The performance is benchmarked against: (1) equally weighted and (2) market-cap weighted investments in all of the ranked assets, as well as against the buy and hold strategies based on (3) S&P500 index, and (4) Bitcoin price. Our results show a clear and significant dominance of the short-term contrarian effect over both momentum effect and the benchmark portfolios. The information ratio coefficient for the contrarian strategies often exceeds two-digit values depending on the assumed reallocation period and the width of the ranking window. Additionally, we observe a significant diversification potential for all cryptocurrency portfolios with relation to the S&P500 index.

2018

• Robert Ślepaczuk, Maryna Zenkova (2018), Robustness of Support Vector Machines in Algorithmic Trading on Cryptocurrency Market, Central European Economic Journal, Volume 5, Pages 186-205

  This study investigates the profitability of an algorithmic trading strategy based on training SVM model to identify cryptocurrencies with high or low predicted returns. A tail set is defined to be a group of coins whose volatility-adjusted returns are in the highest or the lowest quintile. Each cryptocurrency is represented by a set of six technical features. SVM is trained on historical tail sets and tested on the current data. The classifier is chosen to be a nonlinear support vector machine. The portfolio is formed by ranking coins using the SVM output. The highest ranked coins are used for long positions to be included in the portfolio for one reallocation period. The following metrics were used to estimate the portfolio profitability: %ARC (the annualized rate of change), %ASD (the annualized standard deviation of daily returns), MDD (the maximum drawdown coefficient), IR1, IR2 (the information ratio coefficients). The performance of the SVM portfolio is compared to the performance of the four benchmark strategies based on the values of the information ratio coefficient IR1, which quantifies the risk-weighted gain. The question of how sensitive the portfolio performance is to the parameters set in the SVM model is also addressed in this study.

• Przemysław Ryś, Robert Ślepaczuk (2018), Machine Learning Methods in Algorithmic Trading Strategy Optimization – Design and Time Efficiency, Central European Economic Journal, Volume 5, Pages 206-229

  The main aim of this paper was to formulate and analyse the machine learning methods, fitted to the strategy parameters optimization specificity. The most important problems are the sensitivity of a strategy performance to little parameter changes and numerous local extrema distributed over the solution space in an irregular way. The methods were designed for the purpose of significant shortening of the computation time, without a substantial loss of strategy quality. The efficiency of methods was compared for three different pairs of assets in case of moving averages crossover system. The problem was presented for three sets of two assets’ portfolios. In the first case, a strategy was trading on the SPX and DAX index futures; in the second, on the AAPL and MSFT stocks; and finally, in the third case, on the HGF and CBF commodities futures. The methods operated on the in-sample data, containing 16 years of daily prices between 1998 and 2013 and was validated on the out-of-sample period between 2014 and 2017. The major hypothesis verified in this paper is that machine learning methods select strategies with evaluation criterion near the highest one, but in significantly lower execution time than the brute force method (Exhaustive Search).

• Przemysław Ryś, Robert Ślepaczuk (2018), Machine learning in algorithmic trading strategy optimization – implementation and efficiency, Working Papers 2018-25, Faculty of Economic Sciences, University of Warsaw

  The main aim of this paper was to formulate and analyze the machine learning methods, fitted to the strategy parameters optimization specificity. The most important problems are the sensitivity of a strategy performance to little parameter changes and numerous local extrema distributed over the solution space in an irregular way. The methods were designed for the purpose of significant shortening of the computation time, without a substantial loss of a strategy quality. The efficiency of methods was compared for three different pairs of assets in case of moving averages crossover system. The methods operated on the in sample data, containing 20 years of daily prices between 1998 and 2017. The problem was presented for three sets of two assets portfolios. In the first case, a strategy was trading on the SPX and DAX index futures, in the second on the AAPL and MSFT stocks and finally, in the third case on the HGF and CBF commodities futures. The major hypothesis verified in this thesis is that machine learning methods select strategies with evaluation criterion near to the highest one, but in significantly lower execution time than the Exhaustive Search.

• Robert Ślepaczuk, Paweł Sakowski, Grzegorz Zakrzewski (2018), Investment strategies beating the market. What can we squeeze from the market?, eFinanse Vol.14, no. 4, s. 36-55

  The paper presents a new approach to optimizing automatic transactional systems. We propose a multi-stage technique which enables us to find investment strategies beating the market. Additionally, new measures of combined risk and returns are applied in the process of optimization. Moreover, we define new elements of a risk control system based on volatility measures and consecutive signal confirmation. As a result, we formulate three complex investment systems which maximize returns and simultaneously minimize risk in comparison to all other alternative investments (IR=2, Maximum Drawdown<21%, Maximum Loss Duration=0.75 year). Our analysis is based on historical daily data (1998-2010, in- and out-of-sample period) for index and commodity futures. Afterwards, the systems are reoptimized and reallocated each half a year in order to include the most recent financial data. Finally, we show the results for a joint model consisting of our three systems.

• Małgorzata Jabłczyńska, Krzysztof Kosc, Przemysław Ryś, Robert Ślepaczuk, Paweł Sakowski, Grzegorz Zakrzewski (2018), Why you should not invest in mining endeavour? The efficiency of BTC mining under current market conditions, Working Papers 2018-18, Faculty of Economic Sciences, University of Warsaw

  The main aim of this paper is to analyse the efficiency of BTC mining under current market conditions. After thorough analysis of initial assumptions concerning the (1) price of mining machine and its effective amortization period, (2) difficulty and hash rate of BTC network, (3) BTC transaction fees and (4) energy costs, we have found that currently BTC mining is not profitable, except for some rare cases. The main reason of this phenomenon is the fast and unpredictable increase of difficulty of BTC network over time which results in decreasing participation of our mining machines in BTC network hash rate. The research is augmented with detailed sensitivity analysis of mining efficiency to initial parameters assumptions, which allows to observe that the conditions for BTC mining to be efficient and profitable are very challenging to meet.

2014

• Piotr Arendarski, Paweł Misiewicz, Mariusz Nowak, Tomasz Skoczylas, and Robert Wojciechowski (2014), Generalized Momentum Asset Allocation Model, Working Papers 2014-30, Faculty of Economic Sciences, University of Warsaw

  In this paper we propose Generalized Momentum Asset Allocation Model (GMAA). GMAA is a new approach to construct optimal portfolio and is based on close examination of asset’s returns distribution. GMAA tries to capture certain market phenomena and use information they contain as predictors for future returns. Our model is validated using MSCI Indexes with MSCI World Index set as a benchmark. We find results rather promising as we managed to significantly reduce portfolio volatility and obtain stable path of cumulative returns of portfolio. Our model outperforms benchmark in terms of Information Ratio or Maximum Drawdown. Detailed sensitivity analysis was conducted at the end of this paper and it shows that our strategy is sensitive to a few optimization parameters thus further research may be required.

• Tomasz Skoczylas (2014), Modeling Volatility with Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity model, Working Papers 2014-06, Faculty of Economic Sciences, University of Warsaw.

  In this paper a new ARCH-type volatility model is proposed. The Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity (RHARCH) model draws inspiration from Heterogeneous Autoregressive Conditional Heteroskedasticity presented by Muller et al. (1995), but employs more efficient, range-based volatility estimators instead of simple squared returns in conditional variance equation. In the first part of this research range-based volatility estimators (such as Parkinson, or Garman-Klass estimators) are reviewed, followed by derivation of the RHARCH model. In the second part of this research the RHARCH model is compared with selected ARCH-type models with particular emphasis on forecasting accuracy. All models are estimated using data containing EURPLN spot rate quotation. Results show that RHARCH model often outperforms return-based models in terms of predictive abilities in both in-sample and out-of-sample periods. Also properties of standardized residuals are very encouraging in case of the RHARCH model.

• Juliusz Jabłecki & Ryszard Kokoszczyński & Paweł Sakowski & Robert Ślepaczuk & Piotr Wójcik (2014), Does historical volatility term structure contain valuable in-formation for predicting volatility index futures?, Working Papers 2014-18, Faculty of Economic Sciences, University of Warsaw.

  We suggest that the term structure of volatility futures (e.g. VIX futures) shows a clear pattern of dependence on the current level of VIX index. At the low level of VIX (below 20) the term structure is highly upward sloping; at the high VIX level (over 30) it is strongly downward sloping. We use those features to better predict future volatility and index futures. We begin by introducing some quantitative measures of volatility term structure (VTS) and volatility risk premium (VRP). We use them further to estimate the distance between the actual value and the fair (model) value of the VTS. We find that this distance has significant predictive power for volatility futures and index futures and we use this feature to design a simple strategy to invest in VIX index futures and S&P500.

• Juliusz Jabłecki & Ryszard Kokoszczyński & Paweł Sakowski & Robert Ślepaczuk & Piotr Wójcik (2014) Options delta hedging with no options at all, Working Papers 2014-27, Faculty of Economic Sciences, University of Warsaw.

  The adjustment speed of delta hedged options exposure depends on the market realized and implied volatility. We observe that by consistently hedging long and short positions in options we can eventually end up with pure exposure to volatility without any options in the portfolio at all. The results of such arbitrage strategy is based only on speed of adjustment of delta hedged option positions. More specifically, they rely on interrelation between realized volatility levels calculated for various time intervals (from daily to intraday frequency). Theoretical intuition enables us to solve the puzzle of the optimal frequency of hedge adjustment and its influence on hedging efficiency. We present results of a simple hedge strategy based on the consistent hedging of a portfolio of options for various worldwide equity indices.

• Juliusz Jabłecki & Ryszard Kokoszczyński & Paweł Sakowski & Robert Ślepaczuk & Piotr Wójcik (2014), Volatility as a new class of assets? The advantages of using volatility index futures in investment strategies, Working Papers 2014-26, Faculty of Economic Sciences, University of Warsaw.

  This paper investigates the changes in the investment portfolio performance after including VIX. We apply different models for optimal portfolio selection (Markowitz and Black-Litterman) assuming both the possibility of short sale and the lack of it. We also use various assets, data frequencies, and investment horizons to get a comprehensive picture of our results’ robustness. Investment strategies including VIX futures do not always deliver higher returns or higher Sharpe ratios for the period 2006-2013. Their performance is quite sensitive to changes in model parameters. However, including VIX significantly increases the returns in almost all cases during the recent financial crisis. This result clearly emphasizes potential gains of having such an asset in the portfolio in case of very high volatility in financial markets.

• Juliusz Jabłecki, Ryszard Kokoszczyński, Paweł Sakowski, Robert Ślepaczuk and Piotr Wójcik ( 2014), Simple heuristics for pricing VIX options, Working Papers 2014-25, Faculty of Economic Sciences, University of Warsaw.

  The article presents a simple parameterization of the volatility surface for options on the S&P 500 volatility index, VIX. Specifically, we document the following features of VIX implied volatility: (i) VIX at-the-money (ATM) implied volatility correlates strongly with the volatility skew in S&P 500 options; (ii) VIX ATM implied volatility declines exponentially with options’ time to expiry; (iii) a SABR-type model can be used to model the smile observed in VIX options. These observations lead to simple heuristics for quoting prices (in terms of implied volatility) of VIX options with almost arbitrary strike and expiry, obtaining values that are reasonably close to market levels.

• Alexandros Agapitos, Michael O’Neill, Piotr Arendarski, Anthony Brabazon (2014), Forward Stagewise Additive Modelling for High Frequency Trading, University College Dublin, preprint submitted to Information Sciences Journal

  Forecasting time-series of high-frequency asset returns is an essential part of modern trading systems. Forward Stagewise Additive Modelling (FSAM) is a powerful Machine Learning method that has been successfully applied to function estimation tasks. It is an iterative procedure that fits an additive expansion in a set of basis functions; the basis function that best fits the current residuals is added to the expansion at each step. The goal of this paper is to propose an extension to the standard FSAM method, and empirically demonstrate its efficiency in the domain of high-frequency financial time-series modelling. The two principal components of the extended modelling method are a hyperbolic tangent transformation of the first-level residuals that addresses the issue of robust estimation, and a linear bias correction of the final model. Results on the GBP/USD foreign exchange, S&P500, and GOLD spot-price time-series of five-minutes and one-hour frequencies suggest that for the majority of problems the proposed method performs better out-of-sample when compared against traditional linear and non-linear time-series modelling methods and their ensemble versions, as well as an adaptation of FSAM found in the literature.

2012

• Piotr Arendarski & Łukasz Postek (2012), Cointegration Based Trading Strategy For Soft Commodities Market, University of Warsaw, Faculty of Economic Sciences, Working Paper

  This paper explores cointegration among three of the most popular agriculture soft commodities (corn, soya and wheat) and its potential usefulness for dynamic asset allocation strategies. Johansen tests indicate that natural logarithms of weekly prices of corn, soya and wheat futures are cointegrated and two cointegrating vectors exist. Formal tests show that the estimated long-run relationship is stable even beyond the estimation sample. We use obtained results to create simple trading rules and verify their profitability. The trading strategies’ risk-adjusted abnormal returns look to be significant based on the Sharpe ratio criterion and they are low correlated with the stock market.

• Piotr Arendarski (2012), Tactical allocation in falling stocks: Combining momentum and solvency ratio signals, University of Warsaw, Faculty of Economic Sciences, Working Paper

  We identified 4500 US stocks with year ending losses of 50 percent or more during the 2001-2011 period. We screened our “falling knives” for financial strength to promote a greater likelihood of recovery and minimize any survivorship bias. We added the constraints of Altman Z-Scores, debt/equity ratio, and current ratio to our data set. We use GARCH-in-mean model to control the risk of the strategies. The results show consistent improvement of risk-standardized return profiles of the strategies in comparison with buy and hold strategy.

• Robert Ślepaczuk, Grzegorz Zakrzewski, Paweł Sakowski (2012), Investment strategies beating the market. What can we squeeze from the market? University of Warsaw, Faculty of Economic Sciences, Working Paper

  The paper presents the new approach to optimizing automatic transactional systems. We propose the multi-stage technique which enables us to find investment strategies beating the market. Additionally, new measures of combined risk and returns are applied in the process of optimization. Moreover, we define new elements of risk control system based on volatility measures and consecutive signals confirmation. As the result, we formulate three complex investment systems, which maximize returns and simultaneously minimize risk in comparison to all other alternative investments (IR=2, Maximum Drawdown<21%, Maximum Loss Duration=0.75 year). Our analysis is based on historical daily data (1998-2010, in- and out-ofsample period) for index and commodity futures. Afterwards, systems are reoptimized and reallocated each half a year in order to include the most recent financial data. Finally, we show the results for joint model consisting of our three systems.

• Paweł Sakowski, Robert Ślepaczuk, Ryszard Kokoszczyński (2012), Option Pricing Models with HF Data: An Application of the Black Models to the WIG20 Index, Journal of CENTRUM Cathedra.

  In this paper, we compared several Black option pricing models by applying different measures of volatility and examined the Black model with historical (BHV), implied (BIV), and several different types of realized (BRV) volatility. The main objective of the study was to find the best model; that is, the model that predicts the actual market price with the minimum error. The high frequency (HF) data and bid-ask quotes (instead of transactional data) for the Warsaw Stock Exchange (WSE) were used to omit the problem of nonsynchronous trading and to increase the number of observations. Several error statistics and the percentage of price overpredictions (OP) showed the results that confirmed the initial intuition that the BIV model is the best model, the BHV model is the second best, and the BRV is the least efficient among the models studied.

2010

• Paweł Sakowski, Robert Ślepaczuk, Ryszard Kokoszczyński (2010), Which Option Pricing Model is the Best? High Frequency Data for Nikkei 225 Index Options, University of Warsaw, Faculty of Economic Sciences, Working Paper

  Option pricing models are the main subject of many research papers prepared both in academia and financial industry. Using high-frequency data for Nikkei225 index options, we check the properties of option pricing models with different assumptions concerning the volatility process (historical, realized, implied, stochastic or based on GARCH model). In order to relax the continuous dividend payout assumption, we use the Black model for pricing options on futures, instead of the Black-Scholes-Merton model. The results are presented separately for 5 classes of moneyness ratio and 5 classes of time to maturity in order to show some patterns in option pricing and to check the robustness of our results. The Black model with implied volatility (BIV) comes out as the best one. Highest average pricing errors we obtain for the Black model with realized volatility (BRV). As a result, we do not see any additional gain from using more complex and time-consuming models (SV and GARCH models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare our results with a detailed study for the emerging market of WIG20 index options.

• Paweł Sakowski, Robert Ślepaczuk, Ryszard Kokoszczyński (2010), Midquotes or Transactional Data? The Comparison of Black Model on HF Data, University of Warsaw, Faculty of Economic Sciences, Working Paper

  The main idea of this research is to check the efficiency of the Black option pricing model on the basis of HF emerging market data. However, liquidity constraints – a typical feature of an emerging derivatives market – put severe limits for conducting such a study. That is the reason why Kokoszczynski et al., 2010, have conducted their earlier research on midquotes data treating them as potential transactional data. They have got some intriguing conclusions about implementing different volatility processes into the Black option model. Nevertheless, taking into account that midquotes do not have to be the proper representation of market prices as probably transactional data do, we decide to compare in this paper the results of the research conducted on HF transactional and midquotes data. This comparison shows that the results do not differ significantly between these two approaches and that BIV model significantly outperforms other models, especially BRV model with the latter producing the worst results. Additionally, we provide the discussion of liquidity issue in the context of emerging derivatives market. Finally, after exclusion of spurious outliers we observe significant patterns in option pricing that are not visible on the raw data.

• Paweł Sakowski, Robert Ślepaczuk, Ryszard Kokoszczyński (2010), Option Pricing Models with HF Data – a Comparative Study. The Properties of Black Model with Different Volatility Measures, University of Warsaw, Faculty of Economic Sciences, Working Paper

  This paper compares option pricing models, based on Black model notion (Black, 1976), especially focusing on the volatility models implied in the process of pricing. We calculated the Black model with historical (BHV), implied (BIV) and several different types of realized (BRV) volatility (additionally searching for the optimal interval Δ, and parameter n – the memory of the process). Our main intention was to find the best model, i.e. which predicts the actual market price with minimum error. We focused on the HF data and bidask quotes (instead of transactional data) in order to omit the problem of non-synchronous trading and additionally to increase the significance of our research through numerous observations. After calculation of several error statistics (RMSE, HMAE and HRMSE) and additionally the percent of price overpredictions, the results confirmed our initial intuition that that BIV is the best model, BHV being the second best, and BRV – the least efficient of them. The division of our database into different classes of moneyness ratio and TTM enabled us to observe the distinct differences between compared pricing models. Additionally, focusing on the same pricing model with different volatility processes results in the conclusion that point-estimate, not averaged process of RV is the main reason of high errors and instability of valuation in high volatility environment. Finally, we have been able to detect “spurious outliers” and explain their effect and the reason for them owing to the multi-dimensional comparison of the pricing error statistics.

2009

• Robert Ślepaczuk, Grzegorz Zakrzewski (2009), High-Frequency and Model-Free Volatility Estimators, University of Warsaw, Faculty of Economic Sciences, Working Paper

  This paper focuses on volatility of financial markets, which is one of the most important issues in finance, especially with regard to modeling high-frequency data. Risk management, asset pricing and option valuation techniques are the areas where the concept of volatility estimators (consistent, unbiased and the most efficient) is of crucial concern. Our intention was to find the best estimator of true volatility taking into account the latest investigations in finance literature. Basing on the methodology presented in Parkinson (1980), Garman and Klass (1980), Rogers and Satchell (1991), Yang and Zhang (2000), Andersen et al. (1997, 1998, 1999a, 199b), Hansen and Lunde (2005, 2006b) and Martens (2007), we computed the various model-free volatility estimators and compared them with classical volatility estimator, most often used in financial models. In order to reveal the information set hidden in high-frequency data, we utilized the concept of realized volatility and realized range. Calculating our estimator, we carefully focused on ? (the interval used in calculation), n (the memory of the process) and q (scaling factor for scaled estimators). Our results revealed that the appropriate selection of ? and n plays a crucial role when we try to answer the question concerning the estimator efficiency, as well as its accuracy. Having nine estimators of volatility, we found that for optimal n (measured in days) and ? (in minutes) we obtain the most efficient estimator. Our findings confirmed that the best estimator should include information contained not only in closing prices but in the price range as well (range estimators). What is more important, we focused on the properties of the formula itself, independently of the interval used, comparing the estimator with the same ?, n and q parameter. We observed that the formula of volatility estimator is not as important as the process of selection of the optimal parameter n or ?. Finally, we focused on the asymmetry between market turmoil and adjustments of volatility. Next, we put stress on the implications of our results for well-known financial models which utilize classical volatility estimator as the main input variable.

• Robert Ślepaczuk, Grzegorz Zakrzewski, Emerging versus developed volatility indices (2009). The comparison of VIW20 and VIX indices, University of Warsaw, Faculty of Economic Sciences, Working Paper

  Modeling of financial markets volatility is one of the most significant issues of contemporary finance, especially with regard to analyzing high-frequency data. Accurate quantification and forecast of volatility are of immense importance in risk management (VaR models, stress testing and worst-case scenario), models of capital market and options valuation techniques. What we show in this paper is the methodology for calculating volatility index for Polish capital market (VIW20 ? index anticipating expected volatility of WIG20 index). The methods presented are based on VIX index (VIX White Paper, 2003) and enriched with necessary modifications corresponding to the character of Polish options market. Quoted on CBOE, VIX index is currently known as the best measure of capital investment risk perfectly illustrating the level of fear and emotions of market participants. The conception of volatility index is based on the combination of realized volatility and implied volatility which, using methodology of Derman et al. (1999) and reconstructing volatility surface, reflects both volatility smile as well as its term structure. The research is carried out using high-frequency data (i.e. tick data) for index options on WIG20 index for the period November 2003 – May 2007, in other words, starting with the introduction of options by Warsaw Stock Exchange. All additional simulations are carried out using data gathered in years 1998-2008. Having analyzed VIW20 index in detail, we observed its characteristic behavior during the periods of strong market turmoils. What we also present is the analysis of the influence of VIW20 and VIX index-based instruments both on construction of minimum risk portfolio and on the quality of derivatives portfolio management in which volatility risk and liquidity risk play a key role. The main objective of this paper is to provide foundations for introducing appropriate volatility indices and volatility-based derivatives. This is done with paying attention to crucial methodology changes, necessary if one considers strong markets inefficiencies in emerging countries. As the introduction of appropriate instruments will enable active management of risks that are unhedgable nowadays it will significantly contribute to the development of the given markets in the course of time. In the summary we additionally point to the benefits Warsaw Stock Exchange might obtain from, being one of the few emerging markets possessing appropriately quantified investment risk as well as derivatives to manage it.

2008

• Robert Ślepaczuk, Paweł Strawiński (2008), Analysis of HF data on the WSE in the context of EMH, University of Warsaw, Faculty of Economic Sciences, Working Paper

  This paper focuses on one of the heavily tested issue in the contemporary finance, i.e. efficient market hypothesis (EMH). The existing evidence in the literature is ambiguous. For some markets the departure from efficiency is observed only when High Frequency (HF) data are analysed. Therefore, we verify efficient market hypothesis (EMH) basing our analysis on 5-minute data for WIG20 index futures quoted on the Warsaw Stock Exchange (WSE). We use robust regression that assigns the higher weights to the better behaved observations in order to verify the existence of daily and hourly effects. Our results indicate that the day of the week effect and hour of the day effect are observed. What is more important is the existence of strong open jump effect for all days except Wednesday and positive day effect for Monday. Considering the hour of the day effect we observe positive, persistent and significant open jump effect and the end of session effect. Aforementioned results confirm our initial hypothesis that Polish stock market is not efficient in the information sense.