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Review of Finance
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Article . 1999
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Article . 1998 . Peer-reviewed
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Review of Finance
Article . 1999 . Peer-reviewed
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Research . 1998
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Stochastic Volatility With an Ornstein-Uhlenbeck Process: An Extension

Stochastic volatility with an Ornstein-Uhlenbeck process: an extension
Authors: Schöbel, Rainer; Zhu, Jianwei;

Stochastic Volatility With an Ornstein-Uhlenbeck Process: An Extension

Abstract

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

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Keywords

ddc:330, Stochastic models in economics, Börsenkurs, Volatilität, Stochastischer Prozess, Derivative securities (option pricing, hedging, etc.), mean-reversion, volatility smile, Fourier inversion, Optionspreistheorie, stochastic volatility, Ornstein-Uhlenbeck process, option pricing, Theorie

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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    286
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
286
Top 1%
Top 1%
Average
bronze