Research ArticleOpen AccessGoogle Scholar indexed
An Empirical Study of Option Prices under the Hybrid Brownian Motion Model
Faculty of Business Administration, Kyoto Sangyo University, Kyoto, Japan
Finance Division, Citigroup Global Markets Japan, Tokyo, Japan
- 1 Faculty of Business Administration, Kyoto Sangyo University, Kyoto, Japan
- 2 Finance Division, Citigroup Global Markets Japan, Tokyo, Japan
Journal of Mathematical Finance·Volume 03 (2013)·Pages 329–334·Published 24 May 2013·DOI10.4236/jmf.2013.32033
Copy link · social · email
Abstract
In this paper, we mainly discuss an empirical study of option prices under the hybrid Brownian motion model devel oped by [1]. In a specific case of parameters, we have a simple transition probability density function that has a fat tailed feature as time passes. We show some empirical evidences that the feature of the model reflects the real market price movements in Japanese stock market. Furthermore, we make a performance comparison between the hybrid model and the BS model using Nikkei 225 call options. In general our results show that the hybrid model is slightly better than the BS model.
KeywordsHybrid Brownian MotionsFat-Tailed PropertiesNon-Normal DistributionEmpirical StudiesNikkei 225 Index Options
- W. T. Shaw and M. Schofield, “A Model of Returns for the Post-credit-crunch Reality: Hybrid Brownian Motion with Price Feedback,” Quantitative Finance, 2012, pp. 1-24. doi:10.1080/14697688.2011.642810
- B. Mandelbrot, “The Variation of Certain Speculative Prices,” Journal of Business, Vol. 36, No. 4, 1963, pp. 394-419. doi:10.1086/294632
- E. F. Fama, “The Behavior of Stock-market Prices,” Journal of Business, Vol. 38, No. 1, 1965, pp. 34-105. doi:10.1086/294743
- R. C. Blattberg and H. J. Gonedes, “A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices,” Journal of Business, Vol. 47, No. 2, 1974, pp. 244-280. doi:10.1086/295634
- K. Aas and I. H. Haff, “The Generalized Hyperbolic Skew Student T-distribution,” Journal of Financial Econometrics, Vol. 4, No. 2, 2006, pp. 275-309. doi:10.1093/jjfinec/nbj006
- Y. Nagahara, “Non-Gaussian Distribution for Stock Returns and Related Stochastic Differential Equation,” AsiaPacific Financial Markets, Vol. 3, 1996, pp. 121-149.
- M. Rubinstein, “Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Options Classes from August 23, 1976 through August 31, 1978,” Journal of Finance, Vol. 40, No. 2, 1985, pp. 455-480. doi:10.1111/j.1540-6261.1985.tb04967.x
- J. Hull and A. White, “The Pricing of Options on Assets with Stochastic Volatilities,” Journal of Finance, Vol. 42, No. 2, 1987, pp. 281-300. doi:10.1111/j.1540-6261.1987.tb02568.x
- S. Heston, “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” Review of Financial Studies, Vol. 6, No. 2, 1993, pp. 327-343. doi:10.1093/rfs/6.2.327
- G. Bakshi, C. Cao and Z. Chen, “Empirical Performance of Alternative Option Pricing Models,” Journal of Finance, Vol. 52, No. 5, 1997, pp. 2003-2049. doi:10.1111/j.1540-6261.1997.tb02749.x
- B. Dupire, “Pricing with a Smile,” Risk, Vol. 7, 1994, pp. 18-20.