A Study of Option Pricing Using Variance Gamma Process

Title & Authors
A Study of Option Pricing Using Variance Gamma Process
Lee, Hyun-Eui; Song, Seong-Joo;

Abstract
Option pricing models using L$\small{\acute{e}}$evy processes are suggested as an alternative to the Black-Scholes model since empirical studies showed that the Black-Sholes model could not reflect the movement of underlying assets. In this paper, we investigate whether the Variance Gamma model can reflect the movement of underlying assets in the Korean stock market better than the Black-Scholes model. For this purpose, we estimate parameters and perform likelihood ratio tests using KOSPI 200 data based on the density for the log return and the option pricing formula proposed in Madan et al. (1998). We also calculate some statistics to compare the models and examine if the volatility smile is corrected through regression analysis. The results show that the option price estimated under the Variance Gamma process is closer to the market price than the Black-Scholes price; however, the Variance Gamma model still cannot solve the volatility smile phenomenon.
Keywords
Black-Scholes model;L$\small{\acute{e}}$vy processes;Variance Gamma process;option pricing model;
Language
Korean
Cited by
1.
블랙-숄즈 모형과 Variance Gamma 모형을 이용한 지수연동예금 수익률 예상,김치훈;송성주;

Journal of the Korean Data Analysis Society, 2012. vol.14. 5, pp.2463-2475
References
1.
Bates, D. (1995). Post-Crash Moneyness Biases in S&P500 Futures Options, Rodney, L., White Center Working Paper, Wharton School, University of Pennsylvania, Philadelphia, PA.

2.
Buraschi, A. and Jackwerth, J. (2001). The price of a smile: Hedging and spanning in option markets, Review of Financial Studies, 14, 495-527.

3.
Carr, P., Geman, H., Madan, D. and Yor, M. (2002). The fine structure of asset returns: An empirical investigation, Journal of Business, 75, 305-333.

4.
Elliot, R., Lahaie, C. and Madan, D. (1995). Filtering derivative security valuations from market prices, In Proceedings of the Issac Newton Workshop in Financial Mathematics, Cambridge University Press.

5.
Geman, H. (2002). Pure jump L´evy processes for asset pricing modelling, Journal of Banking and Finance, 26, 1297-1316.

6.
Jacquier, E. and Jarrow, R. (1995). Dynamic Evaluation of Contingent Claim Models: An Analysis of Model Error, Working Paper, Johnson Graduate School of Management, Cornell University, Ithaca, New York.

7.
Kou, S. G. (2002). A jump diffusion model for option pricing, Management Science, 48, 1086-1101.

8.
Madan, D., Carr, P. and Chang, E. (1998). The variance gamma process and option pricing, European Finance Review, 2, 79-105.

9.
Madan, D. and Milne, F. (1991). Option pricing with variance gamma martingale components, Mathematical Finance, 1, 39-55.

10.
Maekawa, K., Lee, S., Morimoto, T. and Kawai, K. (2008). Jump diffusion model: An application to the Japanese stock market, Mathematics and Computers in Simulation, 78, 223-236.

11.
Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3, 125-144.