RFS Advance Access published online on October 9, 2009
Review of Financial Studies, doi:10.1093/rfs/hhp078
Option Valuation with Conditional Heteroskedasticity and Nonnormality
McGill University, CBS, and CREATES
University of Iowa
Duke University
University of Houston, McGill University, and Tilburg University
Send correspondence to Peter Christoffersen, Desautels Faculty of Management, McGill University, 1001 Sherbrooke Street West, Montreal, Quebec, Canada H3A 1G5; telephone: (514) 398-2869; fax: (514) 398-3876. E-mail: peter.christoffersen{at}mcgill.ca
JEL Classification: G12
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Abstract |
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We provide results for the valuation of European-style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite state space setup using the no-arbitrage principle and an equivalent martingale measure (EMM). Our approach allows for general forms of heteroskedasticity in returns, and valuation results for homoskedastic processes can be obtained as a special case. It also allows for conditional nonnormal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of EMMs for which the resulting risk-neutral return dynamics are from the same family of distributions as the physical return dynamics. In this case, our framework nests the valuation results obtained by Duan (1995) and Heston and Nandi (2000) by allowing for a time-varying price of risk and nonnormal innovations. We provide extensions of these results to more general EMMs and to discrete-time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous-time models.
Christoffersen and Jacobs are also affiliated with CIRANO and CIREQ and want to thank Fonds de recherche sur la société et la culture (FQRSC), Institut de Finance Mathématique de Montréal (IFM2), and Social Sciences and Humanities Research Council (SSHRC) for financial support. Elkamhi and Feunou were supported by grants from IFM2. For helpful comments we thank Tomas Bjork, Tim Bollerslev, Mo Chaudhury, Rene Garcia, Anders Kock, Tom McCurdy, Nour Meddahi, Karim Mimouni, Eric Renault, Marcel Rindisbacher, Raman Uppal (the Editor), and an anonymous referee. Any remaining inadequacies are ours alone.