Option Valuation with Conditional Skewness

44 Pages Posted: 23 Jun 2004

See all articles by Peter Christoffersen

Peter Christoffersen

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

Steven L. Heston

University of Maryland - Department of Finance

Kris Jacobs

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

Date Written: July 15, 2003

Abstract

There is extensive empirical evidence that index option prices systematically differ from Black-Scholes prices. Out-of-the-money put prices (and in-the-money call prices) are relatively high compared to the Black-Scholes price. Motivated by these empirical facts, we develop a new discrete-time dynamic model of stock returns with Inverse Gaussian innovations. The model allows for conditional skewness as well as conditional heteroskedasticity and a leverage effect. We present an analytic option pricing formula consistent with this stock return dynamic. An extensive empirical test of the model using S&P500 index options shows that the new Inverse Gaussian GARCH model's performance is superior to a standard existing nested model for out-of-the money puts, thus demonstrating the importance of conditional skewness. The discrete-time Inverse Gaussian GARCH process has two interesting continuous-time limits. One limit is the standard stochastic volatility model of Heston (1993). The other is a pure jump process with stochastic intensity. Using these limit results, an equivalent motivation for our model is that it generalizes standard stochastic volatility models by allowing for "jumps" and other fat-tailed negative movements in stock returns. The empirical results therefore also demonstrate the importance of jumps for the pricing of out-of-the-money puts.

Keywords: GARCH, out-of-sample, jumps, discrete-time model, continuous-time limit

JEL Classification: G12

Suggested Citation

Christoffersen, Peter and Heston, Steven L. and Jacobs, Kris, Option Valuation with Conditional Skewness (July 15, 2003). EFA 2004 Maastricht Meetings Paper No. 2964. Available at SSRN: https://ssrn.com/abstract=557079 or http://dx.doi.org/10.2139/ssrn.557079

Peter Christoffersen

University of Toronto - Rotman School of Management ( email )

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

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Aarhus University - CREATES

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

Steven L. Heston

University of Maryland - Department of Finance ( email )

Robert H. Smith School of Business
Van Munching Hall
College Park, MD 20742
United States

Kris Jacobs (Contact Author)

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

Houston, TX 77204-6021
United States

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