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arXiv · 0909.4765

Linear stochastic volatility models

Jacek Jakubowski·Maciej Wisniewolski
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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.

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Jacek Jakubowski, Maciej Wisniewolski. 2009-09-25. Linear stochastic volatility models. https://arxiv.org/abs/0909.4765

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