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 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.
|Date of creation:||2010|
|Date of revision:|
|Contact details of provider:|| Postal: ul. Dluga 44/50, 00-241 Warszawa|
Phone: (+48 22) 55 49 144
Fax: (+48 22) 831 28 46
Web page: http://www.wne.uw.edu.pl/
More information through EDIRC
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.:
- Yacine Aït-Sahalia, 2005.
"How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise,"
Review of Financial Studies,
Society for Financial Studies, vol. 18(2), pages 351-416.
- Yacine Ait-Sahalia & Per A. Mykland, 2003. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," NBER Working Papers 9611, National Bureau of Economic Research, Inc.
- 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.
- Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
- Andersen, Torben G, 2000. "Some Reflections on Analysis of High-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 146-53, April.
- 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.
- 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.
- Gago, Mónica & Rubio Irigoyen, Gonzalo & León, Angel & Ferreira García, María Eva, 2002.
"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.
- Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
- 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.
- 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.
- 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.
- 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.
- 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.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Dennis Bams & Thorsten Lehnert & Christian C. P. Wolff, 2009.
"Loss Functions in Option Valuation: A Framework for Selection,"
INFORMS, vol. 55(5), pages 853-862, May.
- 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.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- 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.
When requesting a correction, please mention this item's handle: RePEc:war:wpaper:2010-03. See general information about how to correct material in RePEc.
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.