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European Finance Review 1999 3(1):23-46; doi:10.1023/A:1009803506170
© 1999 by European Finance Association
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Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension

Rainer Schöbel and Jianwei Zhu*

Eberhard-Karls-University Tübingen, College of Economics and Business Administration Mohlstrasse 36, 72074 Tübingen, Germany E-mail: rainer.schoebel{at}uni-tuebingen.de; jianwei.zhu{at}uni-tuebingen.de

In this paper, we reexamine and extend the stochastic volatility model of Stein and Stein (S&S) (1991) where volatility follows a mean–reverting Ornstein–Uhlenbeck process. Using Fourier inversion techniques we are able to allow for correlation between instantaneous volatilities and the underlying stock returns. A closed-form pricing solution for European options is derived and some numerical examples are given. In addition, we discuss the boundary behaviour of the instantaneous volatility at v(t) = 0 and show that S&S do not work with an absolute value process of volatility. JEL Classification: G13

Key Words: Ornstein–Uhlenbeck process • Fourier inversion • option pricing • mean-reversion • volatility smile


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