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 4

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

WP(13/2009)23. High-Frequency and Model-Free Volatility Estimators

Authors: Ślepaczuk Robert, Zakrzewski Grzegorz
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 th…

WP23. High-Frequency and Model-Free Volatility Estimators

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.


Ślepaczuk Robert, Zakrzewski Grzegorz
financial market volatility high-frequency financial data realized volatility and correlation volatility forecasting microstructure bias the opening jump effect the bid-ask bounce autocovariance bias daily patterns of volatility emerging markets
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