Archil Gulisashvili (Ohio University): Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models
This is a joint work with Josep Vives (Barcelona University). We obtain sharp asymptotic formulas with error estimates for the Mellin convolution, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic stock price models. Special examples of mixed models are jump-diffusion models and stochastic volatility models with jumps. Applications are given to the Heston model with double exponential jumps. We make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility at extreme strikes in this model. The asymptotic formulas obtained for the implied volatility contain five explicit terms and error estimates. We will also discuss more examples of mixed models.