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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 driving 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 values of the strike price. This is a joint work with E. M. Stein.

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