An Empirical Comparison of Two Stochastic Volatility Models using Indian Market Data
- 245 Downloads
We conduct an empirical comparison of hedging strategies for two different stochastic volatility models proposed in the literature. One is an asymptotic expansion approach and the other is the risk-minimizing approach applied to a Markov-switched geometric Brownian motion. We also compare these with the Black–Scholes delta hedging strategies using historical and implied volatilities. The derivatives we consider are European call options on the NIFTY index of the Indian National Stock Exchange. We compare a few cases with profit and loss data from a trading desk. We find that for the cases that we analyzed, by far the better results are obtained for the Markov-switched geometric Brownian motion.
KeywordsOption pricing Stochastic volatility Mean reverting Regime switching Risk minimizing
JEL ClassificationC02 C90 G13
We wish to thank Kotak Securities for providing us with options traded data for this paper. We also wish to acknowledge Abhinav Srivastava for some of the preliminary computations done during his summer project. Thanks to the referee for several useful suggestions for improvements to this paper.
- Basak, G. K., Ghosh, M. K., & Goswami, A. (2009). Risk minimizing option pricing for a class of exotic options in a markov modulated market. Working paper.Google Scholar
- Bilmes, J. A., & Gentle, A. (1998, April). Tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models options pricing, interest rates and risk management. International Computer Science Institute Berkeley, CA. Retrieved June, 2008 from http://www.cse.unr.edu/bebis/CS679/Readings/GentleEM.pdf.
- Borak, S., Detlefsen, K., & Härdle, W. (2005). FFT based option pricing. Discussion paper: Center For Applicable Statistics and Economics, Humboldt Universität du Berlin, Germany.Google Scholar
- Carr, P., & Madan, D. B. (1999). Option valuation the using fast fourier transform. Journal of Computational, Finance 2(4), 61–73.Google Scholar
- Cont, R., & Kan, Y. (2011). Dynamic hedging of portfolio credit derivatives. SIAM Journal on Financial Mathematics, 2(1), 112140.Google Scholar
- Fouque, J. P., Papanicolaou, G., & Sircar, K. R. (2000). Stochastic volatility correction to Black–Scholes derivatives in financial markets with stochastic volatility. Cambridge: Cambridge University Press.Google Scholar
- Föllmer, H., & Schweizer, M. (1990). Hedging of contingent claims under incomplete information. In M. H. A. Davis & R. J. Elliott (Eds.), Applied stochastic analysis, stochastic monographs (Vol. 5, pp. 389–414). New York: Gordon and Breach.Google Scholar
- Moodley, N. (2005). The Heston model: A practical approach with Matlab code. B.Sc. thesis. University of the Witwatersrand, Johannesburg, South Africa.Google Scholar
- Poulsen, R., Schenk-Hoppé, K. R., & Ewald, C. (2009). Risk minimization in stochastic volatility models: Model risk and empirical performance. Swiss Finance Institute Research paper no. 07–10.Google Scholar
- Schweizer, M. (2001a). Options pricing. Interest rates and risk management. Cambridge: Cambridge University Press.Google Scholar
- Schweizer, M. (2001b). A guided tour through quadratic hedging approaches. In E. Jouini, J. Cvitanic, & M. Musiela (Eds.), Handbooks in mathematical Finance option pricing, interest rates and risk management (p. 538574). Cambridge: Cambridge University Press.Google Scholar