Linear stochastic volatility models

2009/09/25 by Jacek Jakubowski, Jakubowski, Jacek, Maciej Wiśniewolski +2 · 1 citation
Economics, Econometrics and Finance · Social Sciences · #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Stochastic processes and financial applications #q-fin.CP #q-fin.PR

paper · pdf · doi:10.48550/arxiv.0909.4765

20 pages

arxiv created 2013/05/15 · arxiv updated 2013/05/16

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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• Price sensitivities for a general stochastic volatility model

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