Option Valuation with Conditional Heteroskedasticity and Non-Normality

50 Pages Posted: 8 Feb 2007 Last revised: 13 Aug 2009

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; University of Aarhus - CREATES

Redouane Elkamhi

University of Toronto - Rotman School of Management

Bruno Feunou

Bank of Canada

Kris Jacobs

University of Houston - C.T. Bauer College of Business

Multiple version iconThere are 2 versions of this paper

Date Written: March 11, 2009

Abstract

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. 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 non-normal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of equivalent martingale measures 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 non-normal innovations. We provide extensions of these results to more general equivalent martingale measures and to discrete time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous time models.

Keywords: GARCH, risk-neutral valuation, no-arbitrage, non-normal innovations

JEL Classification: G12

Suggested Citation

Christoffersen, Peter and Elkamhi, Redouane and Feunou, Bruno and Jacobs, Kris, Option Valuation with Conditional Heteroskedasticity and Non-Normality (March 11, 2009). Available at SSRN: https://ssrn.com/abstract=961512 or http://dx.doi.org/10.2139/ssrn.961512

Peter Christoffersen (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5P 3C4
Canada
416-946-5511 (Phone)

HOME PAGE: http://www.christoffersen.com

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

University of Aarhus - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Redouane Elkamhi

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

Bruno Feunou

Bank of Canada ( email )

234 Wellington Street
Ottawa, Ontario K1A 0G9
Canada
613-782-8302 (Phone)

HOME PAGE: http://kamkui.net/

Kris Jacobs

University of Houston - C.T. Bauer College of Business ( email )

Houston, TX 77204-6021
United States

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