Working Papers

Seria wydawnicza WNE WORKING PAPERS prowadzona jest przez WNE UW od 2008 r. i jak dotąd opublikowano w niej ponad 400 prac.

Seria WNE Working Papers służy szybkiemu upowszechnianiu wyników badań prowadzonych na Wydziale Nauk Ekonomicznych UW. Publikowane tu teksty mają charakter wersji roboczych (pre-printów): mogą być uzupełniane lub poprawiane w miarę postępu prac nad tekstem i procesu wydawniczego. Prezentujemy aktualną wersję udostępnioną przez autorów, opatrzoną datą oraz identyfikatorami DOI/ISSN – co ułatwia jej cytowanie i śledzenie kolejnych iteracji. Każdy dokument zachowuje pełne prawa autorskie swoich twórców, a w przypadku późniejszych zmian, autorzy mogą w dowolnym momencie zamieścić zaktualizowany plik lub wskazać miejsce ostatecznego wydania.

Do serii WORKING PAPERS przyjmowane są artykuły pracowników naukowych WNE UW oraz publikacje z konferencji organizowanych na WNE UW. Artykuły powinny dotyczyć ekonomii, mieć charakter oryginalnych prac badawczych, nie być wcześniej publikowane. Przyjmowane są wyłącznie teksty w języku angielskim.

Prace prosimy przesyłać e-mailem na adres: wRIOl+7iY03}GUZsM9kAjat4Q{d]#[oB87VuyZ7{sp7lRb/Fa5sGY*ZlQ

Prosimy przesyłać dwa pliki:

(1) główny tekst bez podania tytułu artykułu oraz autorów (plik DOC/DOCX) oraz

(2) stronę tytułową zawierającą: tytuł opracowania, autorów oraz ich afiliację (plik DOC/DOCX). 

Przed przesłaniem tekstu prosimy zapoznać się z szczegółowymi wymogami edycyjnymi.

Redaktorem wydawniczym serii Working Papers jest dr Maciej Bukowski.

Ilość wyników 8

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

Autorzy: 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(31/2020)337. Variance Gamma Model in Hedging Vanilla and Exotic Options

Autorzy: Bollin Bartłomiej, Ślepaczuk Robert
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…

WP337. Variance Gamma Model in Hedging Vanilla and Exotic Options

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.


Bollin Bartłomiej, Ślepaczuk Robert
Monte Carlo option pricing Variance Gamma BSM model Lévy processes FX market hedging Asian and lookback options

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

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

Autorzy: 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

Autorzy: 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

Autorzy: 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

Autorzy: 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

WP(11/2009)21. Emerging versus developed volatility indices. The comparison of VIW20 and VIX indices.

Autorzy: Ślepaczuk Robert, Zakrzewski Grzegorz
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 mana…

WP21. Emerging versus developed volatility indices. The comparison of VIW20 and VIX indices.

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.


Ślepaczuk Robert, Zakrzewski Grzegorz
financial market volatility high-frequency data realized volatility realized range implied and historical volatility volatility forecasting option pricing models investment strategies portfolio optimization
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