ASYMPTOTIC BEHAVIOR OF DISTRIBUTION DENSITIES IN MODELS WITH STOCHASTIC VOLATILITY. I

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of a geometric Brownian motion and the density of the stock price process in the Hull–White model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the price of an Asian option are obtained.