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Stochastic Volatility Option Pricing

Published online by Cambridge University Press:  06 April 2009

Clifford A. Ball  and
Antonio Roma
Clifford A. Ball
Affiliation:
Owen Graduate School of Management, Vanderbilt University, Nashville, TN 37203
Antonio Roma
Affiliation:
Università di Siena, Facoltà di Scienza Economiche e Bancarie, 53100 Siena, Italy
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Abstract

This paper examines alternative methods for pricing options when the underlying security volatility is stochastic. We show that when there is no correlation between innovations in security price and volatility, the characteristic function of the average variance of the price process plays a pivotal role. It may be used to simplify Fourier option pricing techniques and to implement simple power series methods. We compare these methods for the alternative mean-reverting stochastic volatility models introduced by Stein and Stein (1991) and Heston (1993). We also examine the biases in the Black-Scholes model that are eliminated by allowing for stochastic volatility, and we correct some errors in the Stein and Stein (1991) analysis of this issue.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 29 , Issue 4 , December 1994 , pp. 589 - 607
Copyright
Copyright © School of Business Administration, University of Washington 1994

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