Asymptotic Analysis of Stock Price Distributions
Chapter 6 focuses on the asymptotics of stock price densities in classical stochastic volatility models. Sharp asymptotic formulas with relative error estimates for stock price densities in the uncorrelated Hull-White, Stein-Stein, and Heston models due to E.M. Stein and the author are presented in this chapter. The proofs use the asymptotic formulas for mixing distributions and the Abelian theorem for the integral transforms with log-normal kernels established in Chap. 5. Extensions of the asymptotic formulas for the stock price density to the case of the correlated Heston and Stein-Stein models are also presented. The asymptotic behavior of the stock price density in the correlated Hull-White model remains a mystery.
KeywordsSaddle Point Stock Price Asymptotic Formula Stochastic Volatility Model Local Expansion
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