A Linear Stochastic Volatility Model

I introduce a special class of volatility models, namely linear stochastic volatility model. In a linear stochastic volatility model the asset price is linear with respect to the asset itself with coefficient being the stochastic volatility. This class contains among others a log-normal stochastic volatility model.

I give a proof of existence of the density function of asset price and present its probabilistic representation. Moreover, a closed form of the arbitrage price of vanilla options in a linear stochastic volatility model will be given.

This talk is based on joint papers with M. Wisniewolski.