Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension

Rainer Schöbel and Jianwei Zhu

Review of Finance, 1999, vol. 3, issue 1, 23-46

Abstract: 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

Date: 1999
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