Linear stochastic volatility models

Jacek Jakubowski and Maciej Wisniewolski

Papers from arXiv.org

Abstract: In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and Heston stochastic volatility model. For a linear stochastic volatility model we derive representations for the probability density function of the arbitrage price of a financial asset and the prices of European call and put options. A closed-form formulae for the density function and the prices of European call and put options are given for log-normal stochastic volatility model. We also obtain present some new results for Heston and extended Heston stochastic volatility models.

Date: 2009-09, Revised 2013-05
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0909.4765

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