  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.
