Option Pricing Models with HF Data – a Comparative Study. The Properties of Black Model with Different Volatility Measures
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Faculty of Economic Sciences, University of Warsaw in its series Working Papers with number 2010-03.
Length: 33 pages
Date of creation: 2010
Date of revision:
option pricing models; financial market volatility; high-frequency financial data; realized volatility; implied volatility; microstructure bias; emerging markets;
Find related papers by 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 &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-17 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Rubio Irigoyen, Gonzalo & León, Angel & Ferreira García, María Eva & Gago, Mónica, 2003.
"An empirical comparison of the performance of alternative option pricing models,"
DFAEII Working Papers
2002-04, University of the Basque Country - Department of Foundations of Economic Analysis II.
- Eva Ferreira & Mónica Gago & Angel León & Gonzalo Rubio, 2005. "An empirical comparison of the performance of alternative option pricing models," Investigaciones Economicas, Fundación SEPI, vol. 29(3), pages 483-523, September.
- Becker, Ralf & Clements, Adam E. & White, Scott I., 2006. "On the informational efficiency of S&P500 implied volatility," The North American Journal of Economics and Finance, Elsevier, vol. 17(2), pages 139-153, August.
- Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
- Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
- Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
- Christoffersen, Peter & Jacobs, Kris, 2004.
"The importance of the loss function in option valuation,"
Journal of Financial Economics,
Elsevier, vol. 72(2), pages 291-318, May.
- Peter Christoffersen & Kris Jacobs, 2003. "The Importance of the Loss Function in Option Valuation," CIRANO Working Papers 2003s-52, CIRANO.
- Christian Wolff & Dennis Bams & Thorsten Lehnert, 2008.
"Loss Functions in Option Valuation: A Framework for Selection,"
LSF Research Working Paper Series
08-11, Luxembourg School of Finance, University of Luxembourg.
- Dennis Bams & Thorsten Lehnert & Christian C. P. Wolff, 2009. "Loss Functions in Option Valuation: A Framework for Selection," Management Science, INFORMS, vol. 55(5), pages 853-862, May.
- Manuel Ammann & David Skovmand & Michael Verhofen, 2009. "Implied And Realized Volatility In The Cross-Section Of Equity Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 745-765.
- Patrick Dennis & Stewart Mayhew, 2009. "Microstructural biases in empirical tests of option pricing models," Review of Derivatives Research, Springer, vol. 12(3), pages 169-191, October.
- Brandt, Michael W. & Wu, Tao, 2002. "Cross-sectional tests of deterministic volatility functions," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 525-550, December.
- Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
- Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marcin Bąba).
If references are entirely missing, you can add them using this form.