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 10

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(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(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(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(25/2014)142. Simple heuristics for pricing VIX options

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

WP142. Simple heuristics for pricing VIX options

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.


Jabłecki Juliusz, Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert, Wójcik Piotr
VIX VIX options implied volatility surface

WP(18/2014)135. Does historical volatility term structure contain valuable in-formation for predicting volatility index futures?

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

WP135. Does historical volatility term structure contain valuable in-formation for predicting volatility index futures?

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.


Jabłecki Juliusz, Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert, Wójcik Piotr
volatility term structure volatility risk premium volatility and index futures realized volatility implied volatility investment strategies returns forecasting efficient risk and return measures

WP(6/2013)91. The pricing of options on WIG20 using GARCH models

Authors: Kamiński Szymon
In this paper the application of several option pricing models has been tested on the basis of options traded on the Warsaw Stock Exchange. At first, theoretical option prices have been calculated according to the models chosen. Next, the models have…

WP91. The pricing of options on WIG20 using GARCH models

In this paper the application of several option pricing models has been tested on the basis of options traded on the Warsaw Stock Exchange. At first, theoretical option prices have been calculated according to the models chosen. Next, the models have been tested by comparing their option prices estimates to prices observed on the market. The models chosen are: a few alternative versions of the Duan (1995) GARCH Option Pricing Model, and two versions of the model by Black (1976). A separate section is devoted to the impact of the implied dividend yield on prices of options. The study covers a period from January 2006 to March 2012. Results show that the most accurate models are the Black model with a volatility term structure, and the Duan GARCH Option Pricing Model with implied dividend yield and Student's T random errors.


Kamiński Szymon
GARCH models Duan methodology Black model implied volatility option pricing

WP(16/2010)39. Which Option Pricing Model is the Best? High Frequency Data for Nikkei225 Index Options

Authors: Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert
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 co…

WP39. Which Option Pricing Model is the Best? High Frequency Data for Nikkei225 Index Options

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 (Kokoszczyński et al. 2010b).


Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert
option pricing models financial market volatility high-frequency financial data midquotes data transactional data realized volatility implied volatility stochastic volatility microstructure bias emerging markets

WP(15/2010)38. Midquotes or Transactional Data? The Comparison of Black Model on HF Data

Authors: Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert
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 conducti…

WP38. Midquotes or Transactional Data? The Comparison of Black Model on HF Data

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.


Kokoszczyński Ryszard, Sakowski Paweł, Ślepaczuk Robert
option pricing models financial market volatility high-frequency financial data midquotes data transactional data realized volatility implied volatility microstructure bias emerging markets

WP(3/2010)26. Option Pricing Models with HF Data - a Comparative Study. The Properties of Black Model with Different Volatility Measures

Authors: Kokoszczyński Ryszard, Nehrebecka Natalia, Sakowski Paweł, Strawiński Paweł, Ślepaczuk Robert
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 diffe…

WP26. Option Pricing Models with HF Data - a Comparative Study. The Properties of Black Model with Different Volatility Measures

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 - 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.


Kokoszczyński Ryszard, Nehrebecka Natalia, Sakowski Paweł, Strawiński Paweł, Ślepaczuk Robert
option pricing models financial market volatility high-frequency financial data realized volatility implied volatility microstructure bias emerging markets
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