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

Author

Listed:
  • Ryszard Kokoszczyński

    () (Faculty of Economic Sciences, University of Warsaw
    Economic Institute, National Bank of Poland)

  • Natalia Nehrebecka

    () (Faculty of Economic Sciences, University of Warsaw)

  • Paweł Sakowski

    (Faculty of Economic Sciences, University of Warsaw)

  • Paweł Strawiński

    () (Faculty of Economic Sciences, University of Warsaw)

  • Robert Ślepaczuk

    () (Faculty of Economic Sciences, University of Warsaw)

Abstract

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.

Suggested Citation

  • Ryszard Kokoszczyński & Natalia Nehrebecka & Paweł Sakowski & Paweł Strawiński & Robert Ślepaczuk, 2010. "Option Pricing Models with HF Data – a Comparative Study. The Properties of Black Model with Different Volatility Measures," Working Papers 2010-03, Faculty of Economic Sciences, University of Warsaw.
  • Handle: RePEc:war:wpaper:2010-03
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    File URL: http://www.wne.uw.edu.pl/inf/wyd/WP/WNE_WP26.pdf
    File Function: First version, 2010
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    References listed on IDEAS

    as
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    5. Yu, Wayne W. & Lui, Evans C.K. & Wang, Jacqueline W., 2010. "The predictive power of the implied volatility of options traded OTC and on exchanges," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 1-11, January.
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    More about this item

    Keywords

    option pricing models; financial market volatility; high-frequency financial data; realized volatility; implied volatility; microstructure bias; emerging markets;

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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