Stock price distributions with stochastic volatility: an analytic approach

We study the stock price distributions that arise when pricesfollow a diffusion process with a stochastically varying volatilityparameters. We use analytic techniques to derive an explicitclosed-form solution for the case when volatility is drivenby an arithmetic Ornstein-Uhlenbeck (or AR1) process. We thenapply our results to two related problems in the finance literature:(i) options pricing in a world of stochastic volatility, and(ii) the relationship between stochastic volatility and thenature of 'fat tails' in stock price distributions.