Asymptotic behavior of distribution densities in stochastic volatility models
Archil Gulisashvili (Ohio University)
We study the law of stock price processes in several known models with stochastic volatility. These models are the Hull-White, the Stein-Stein,
and the Heston model. It is assumed that standard Brownian motions
the stock price and the volatility equation are independent. Under this
assumption, we find explicit formulas for leading terms in asymptotic
expansions of the stock price distribution density with error estimates.
We also characterize the asymptotic behavior of time averages of
volatility processes. As an application of these results, we get
asymptotic formulas for the implied volatility for large and small
of the strike price. This is a joint work with E. M. Stein.