Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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Number of Results 21

WP(14/2024)450. Construction and Hedging of Equity Index Options Portfolios

Authors: Wysocki Maciej, Ślepaczuk Robert
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 …

WP450. Construction and Hedging of Equity Index Options Portfolios

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.


DOI: https://doi.org/10.33138/2957-0506.2024.14.450
Wysocki Maciej, Ślepaczuk Robert
S&P500 Index options Option Pricing Models Black-Scholes-Merton model Variance-Gamma model Implied Volatility Volatility Risk Premium Volatility Spreads Dynamic Hedging

WP(13/2024)449. The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models

Authors: Natalia Roszyk, Ślepaczuk Robert
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 siz…

WP449. The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models

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.


DOI: https://doi.org/10.33138/2957-0506.2024.13.449
Natalia Roszyk, Ślepaczuk Robert
volatility forecasting LSTM-GARCH S&P 500 index hybrid forecasting models VIX index machine learning financial time series analysis walk-forward process hyperparameters tuning deep learning recurrent neural networks

WP(7/2023)414. The systemic risk approach based on implied and realized volatility

Authors: Sakowski Paweł, Sieradzki Rafał, Ślepaczuk Robert
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 2021 in the USA, Europe, Brazil, and Japan. Our Implied Volatility Realized Volatility Systemic Risk Indicator (I…

WP414. The systemic risk approach based on implied and realized volatility

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 2021 in the USA, Europe, Brazil, and Japan. Our Implied Volatility Realized Volatility Systemic Risk Indicator (IVRVSRI) 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 “the simpler is always better than the more complex, if it leads to the same results”. Such an approach significantly limits the model risk and substantially decreases computational burden. Robustness checks show that IVRVSRI is a precise measure of the current systemic risk in the stock markets. Moreover, IVRVSRI seems to be a valid indication of current systemic risk in equity markets and it can be used for other types of assets and high-frequency data.


Sakowski Paweł, Sieradzki Rafał, Ślepaczuk Robert
systemic risk implied volatility realized volatility volatility indices equity index options market volatility

WP(10/2022)386. Subjective Expectations and Uncertainty

Authors: Kocięcki Andrzej, Łyziak Tomasz, Stanisławska Ewa
Analysis of macroeconomic expectations of private sector agents reveals not only the path of expected macroeconomic developments and the mechanism of expectation formation, but also the degree of uncertainty faced by economic agents. Relying on this …

WP386. Subjective Expectations and Uncertainty

Analysis of macroeconomic expectations of private sector agents reveals not only the path of expected macroeconomic developments and the mechanism of expectation formation, but also the degree of uncertainty faced by economic agents. Relying on this observation the aim of this paper is twofold. First, we lay down the formal theory of subjective expectations and derive the subjective assessment hypothesis, which defines the optimal forecast of an individual under a specific loss function. Keeping the mathematical rigor, the proposed theory attempts to reflect the process of expectation formation that is consistent with well known behavioral features. Second, we apply the subjective assessment hypothesis to pin down the notion of uncertainty. We propose a novel uncertainty index, retrieved from forecast revisions of professional forecasters using an empirical model within the Bayesian approach. The two versions of this index derived for the US—based either on GDP growth or on inflation forecasts—describe different kinds of macroeconomic uncertainty. Their shocks act similarly as demand shocks, pushing economic activity and inflation down.


Kocięcki Andrzej, Łyziak Tomasz, Stanisławska Ewa
Subjective expectations Uncertainty Stochastic volatility Identification Bayesian approach Survey of Professional Forecasters

WP(19/2020)325. Artificial Neural Networks Performance in WIG20 Index Options Pricing

Authors: Wysocki Maciej, Ślepaczuk Robert
In this paper the performance of artificial neural networks in option pricing is analyzed and compared with the results obtained from the Black – Scholes – Merton model based on the historical volatility. The results are compared based on…

WP325. Artificial Neural Networks Performance in WIG20 Index Options Pricing

In this paper the performance of artificial neural networks in option pricing is analyzed and compared with the results obtained from the Black – Scholes – Merton model based on the historical volatility. The results are compared based on various error metrics calculated separately between three moneyness ratios. The market data-driven approach is taken in order to train and test the neural network on the real-world data from the Warsaw Stock Exchange. The artificial neural network does not provide more accurate option prices. 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 differs significantly between moneyness states.


Wysocki Maciej, Ślepaczuk Robert
option pricing machine learning artificial neural networks implied volatility supervised learning index options Black – Scholes – Merton model

WP(10/2020)316. Investing in VIX futures based on rolling GARCH models forecasts

Authors: Bilyk Oleh, Sakowski Paweł, Ślepaczuk Robert
The aim of this work is to compare the performance of VIX futures trading strategies built across different GARCH model volatility forecasting techniques. Long and short signals for VIX futures are produced by comparing one-day ahead volatility forec…

WP316. Investing in VIX futures based on rolling GARCH models forecasts

The aim of this work is to compare the performance of VIX futures trading strategies built across different GARCH model volatility forecasting techniques. Long and short signals for VIX futures are produced by comparing one-day ahead volatility forecasts with current historical volatility. We found out that using the daily data over the seven-year period (2013-2019), strategy based on the fGARCH-TGARCH and GJR-GARCH specifications outperformed those of the GARCH and EGARCH models, and performed slightly below the "buy-and-hold" S&P 500 strategy. For the base GARCH(1,1) model, the training window size and the type gave stable results, whereas the performance across refit frequency, conditional distribution of returns, and historical volatility estimators varies significantly. Despite non-robustness of some investment strategies and some space for improvements, the presented strategies show their potential in competing with the equity and volatility benchmarks.


Bilyk Oleh, Sakowski Paweł, Ślepaczuk Robert
GARCH VIX index volatility futures rolling forecasting volatility investment strategies volatility exposure

WP(14/2019)299. Does the inclusion of exposure to volatility into diversified portfolio improve the investment results? Portfolio construction from the perspective of a Polish investor.

Authors: Latoszek Michał, Ślepaczuk Robert
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 pe…

WP299. Does the inclusion of exposure to volatility into diversified portfolio improve the investment results? Portfolio construction from the perspective of a Polish investor.

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 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 the 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 to answer 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.


Latoszek Michał, Ślepaczuk Robert
Volatility asset class portfolio optimization Polish market Markowitz portfolio naïve diversification

WP(3/2015)151. Bivariate GARCH models for single asset returns

Authors: Skoczylas Tomasz
In this paper an alternative approach to modelling and forecasting single asset returns volatility is presented. A new, bivariate, flexible framework, which may be considered as a development of single-equation ARCH-type models, is proposed. This app…

WP151. Bivariate GARCH models for single asset returns

In this paper an alternative approach to modelling and forecasting single asset returns volatility is presented. A new, bivariate, flexible framework, which may be considered as a development of single-equation ARCH-type models, is proposed. This approach focuses on joint distribution of returns and observed volatility, measured by Garman-Klass variance estimator, and it enables to examine simultaneous dependencies between them. Proposed models are compared with benchmark GARCH and range-based GARCH (RGARCH) models in terms of prediction accuracy. All models are estimated with maximum likelihood method, using time series of EUR/PLN spot rate quotations and WIG20 index. Results are very encouraging especially for foreasting Value-at-Risk. Bivariate models achieved lesser rates of VaR exception, as well as lower coverage tests statistics, without being more conservative than its single-equation counterparts, as their forecasts errors measures are rather similar.


Skoczylas Tomasz
bivariate volatility models joint distribution range-based volatility estimators Garman-Klass estimator observed volatility volatility modelling GARCH leverage Value-at-Risk volatility forecasting

WP(27/2014)144. Options delta hedging with no options at all

Authors: Jabłecki Juliusz, Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert, Wójcik Piotr
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…

WP144. Options delta hedging with no options at all

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 indice


Jabłecki Juliusz, Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert, Wójcik Piotr
options hedging efficiency optimal hedging frequency realized and implied volatility index futures investment strategies

WP(26/2014)143. Volatility as a new class of assets? The advantages of using volatility index futures in investment strategies

Authors: Jabłecki Juliusz, Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert, Wójcik Piotr
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.…

WP143. Volatility as a new class of assets? The advantages of using volatility index futures in investment strategies

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.


Jabłecki Juliusz, Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert, Wójcik Piotr
volatility VIX futures investment strategies optimal portfolio selection Markowitz model Black-Litterman model
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