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By Gulisashvili
Gulisashvili, 2012
This volume centers on the asymptotic analysis of stochastic stock price models. It explores stochastic volatility models, developed to address limitations in the Black-Scholes model. In these models, volatility follows a stochastic process, with examples like the Hull-White, Stein-Stein, and Heston models illustrating different process types. The author provides precise asymptotic formulas with error estimates for distribution densities, option pricing functions, and implied volatilities across various stochastic volatility models. Additionally, sharp asymptotic formulas are established for implied volatility at extreme strikes in general stochastic stock price models.