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

Archil Gulisashvili · Elias M. Stein

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Probability and Risk Models

Abstract

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.

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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1987The Pricing of Options on Assets with Stochastic Volatilities 2003Stochastic Differential Equations 2003Stochastic Differential Equations 1991Stock Price Distributions with Stochastic Volatility: An Analytic Approach 2000Derivatives in Financial Markets with Stochastic Volatility 2008The New Palgrave Dictionary of Economics

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