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Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension (1999)

Schöbel, Rainer ; Zhu, Jianwei

Springer

Review of finance 3 (1999), S. 23-46

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ISSN: 1573-692X

Keywords: Ornstein–Uhlenbeck process ; Fourier inversion ; option pricing ; mean-reversion ; volatility smile

Source: Springer Online Journal Archives 1860-2000

Topics: Economics

Notes: 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 underlyingstock 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1009803506170

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