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Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension

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  • Rainer Schöbel
  • Jianwei Zhu

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

Suggested Citation

  • Rainer Schöbel & Jianwei Zhu, 1999. "Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension," Review of Finance, European Finance Association, vol. 3(1), pages 23-46.
    • Handle: RePEc:oup:revfin:v:3:y:1999:i:1:p:23-46.
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    File URL: http://hdl.handle.net/10.1023/A:1009803506170
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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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