Probabilistic representations of the density function of the asset price and of vanilla options in linear stochastic volatility models

Details Probabilistic representations of the density function of the asset price and of vanilla options in linear stochastic volatility models Probabilistic representations of the density function of the asset price and of vanilla options in linear stochastic volatility models

2009-09-25

arxiv.org/abs/0909.4765v1

Economy

Quantitative Finance

Pricing of Securities

19 pages

Scientific paper

We derive probabilistic representations for the probability density function of the arbitrage price of a financial asset and the price of European call and put options in a linear stochastic volatility model with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. Examples of such models are considered, including a log-normal stochastic volatility model. In all examples a closed formula for the density function is given. In the Appendix we present a conditional version of the Donati-Martin and Yor formula.

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