American option pricing using GARCH models and the normal inverse Gaussian distribution

Journal of Financial Econometrics

Volumn 6, Issue 4, 2008, Pages 540-582

  Stentoft, Lars ^a,b  

^a HEC MONTRÉAL   (Canada)

^b NONE   (Canada)

Author keywords

American options; GARCH models; Least squaresMonte Carlo method; Normal inverse Gaussian distribution

Indexed keywords

EID: 53849144660     PISSN: 14798409     EISSN: 14798417     Source Type: Journal    
DOI: 10.1093/jjfinec/nbn013     Document Type: Article

References (36)

1. Andersson, J. 2001. On the normal inverse Gaussian stochastic volatility model. Journal of Business and Economic Statistics 19: 44-54.
2. Barndorff-Nielsen, O. E. 1997. Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics 24: 1-13.
3. Barndorff-Nielsen, O. E., and N. Shephard. 2001. Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society, Series B 63: 167-241.
4. Black, F., and M. Scholes. 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81: 637-54.
5. Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31: 307-27.
6. Bollerslev, T. 1987. A conditionally heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics 69: 542-7.
7. Bollerslev, T., and H. O. Mikkelsen. 1996. Modelling and pricing long memory in stock market volatility. Journal of Econometrics 73: 151-84.
8. Bollerslev, T., and H. O. Mikkelsen. 1999. Long-term equity anticipation securities and stock market volatility dynamics. Journal of Econometrics 92: 75-99.
9. Carr, P., and L. Wu. 2004. Time-changed Lévy processes and option pricing. Journal of Financial Economics 71: 113-41.
10. Christoffersen, P., S. Heston, and K. Jacobs. 2006. Option valuation with conditional skewness. Journal of Econometrics 131: 253-84.
11. Christoffersen, P., and K. Jacobs. 2004. Which GARCH model for option valuation? Management Science 50: 1204-21.
12. CRSP. 1998. CRSP Stock File Guide. Center for Research in Security Prices, Graduate School of Business, University of Chicago, Chicago, IL.
13. Duan, J.-C. 1995. The GARCH option pricing model. Mathematical Finance 5(1):13-32.
14. Duan, J.-C. "Conditionally Fat-Tailed Distributions and the Volatility Smile in Options." Working paper, Hong Kong University of Science and Technology, 1999.
15. Duan, J.-C., and J.-G. Simonato. 2001. American option pricing under GARCH by a Markov chain approximation. Journal of Economic Dynamics and Control 25: 1689-1718.
16. Duan, J.-C., and H. Zhang. 2001. Pricing Hang Seng Index options around the Asian financial crisis - A GARCH approach. Journal of Banking and Finance 25: 1989-2014.
17. Eberlein, E. 2001. "Application of Generalized Hyperbolic Lévy Motions to Finance." In O. E. Barndorff-Nielsen, T. Mikosch, and S. Resnick eds., Lévy Processes: Theory and Apllications. Boston, MA: Birkhauser, 319-36.
18. Engle, R. F. 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50(4): 987-1007.
19. Engle, R. F., and V. K. Ng. 1993. Measuring and testing the impact of news on volatility. Journal of Finance 48(5): 1749-78.
20. Engle, R., and J. Mezrich. 1996. GARCH for groups. Risk 9(8): 36-40.
21. Forsberg, L., and T. Bollerslev. 2002. Bridging the gap between the distribution of realized (ECU) volatility and ARCH modeling (of the EURO): The GARCH normal i Inverse Gaussian model. Journal of Applied Econometrics 17: 535-48.
22. Hafner, C. M., and H. Herwartz. 2001. Options pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis. Journal of Empirical Finance 8: 1-34.
23. Härdle, W., and C. M. Hafner. 2000. Discrete time option pricing with flexible volatility estimation. Finance and Stochastics 4: 189-207.
24. Heston, S. L. 1993. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6: 327-43.
25. Heston, S. L., and S. Nandi. 2000. A closed-form GARCH option valuation model. Review of Financial Studies 13: 585-625.
26. Hsieh, K. C., and P. Ritchken. 2005. An empirical comparison of GARCH option pricing models. Review of Derivatives Research 8: 129-50.
27. Huang, J.-Z., and L. Wu. 2004. Specification analysis of option pricing models based on time-changed Lévy processes. Journal of Finance LIX(3): 1405-39.
28. Jensen, M. B., and A. Lunde. 2001. The NIG-S&ARCH model: A fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model. Econometrics Journal 4: 319-42.
29. Lambert, P., and S. Laurent. "Modelling Financial Time Series Using GARCH-Type Models with a Skewed Student Distribution for the Innovations." Working paper, Université de Liège, 2001.
30. Lehar, A., M. Scheicher, and C. Schittenkopf. 2002. GARCH vs. stochastic volatility: Option pricing and risk management. Journal of Banking and Finance 26: 323-45.
31. Lehnert, T. 2003. Explaining smiles: GARCH option pricing with conditional leptokurtosis and skewness. Journal of Derivatives 10: 27-39.
32. Longstaff, F. A., and E. S. Schwartz. 2001. Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies 14: 113-47.
33. Merton, R. C. 1973. Theory of rational option pricing. Bell Journal of Economics and Management Science 4: 141-83.
34. Nelson, D. B. 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59: 347-70.
35. Ritchken, P., and R. Trevor. 1999. Pricing options under generalized GARCH and stochastic volatility processes. Journal of Finance 59: 377-402.
36. Stentoft, L. 2005. Pricing American options when the underlying asset follows GARCH processes. Journal of Empirical Finance 12: 576-611.