On Error Estimates for Asymptotic Expansions with Malliavin Weights -- Application to Stochastic Volatility Model

Abstract

This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More generally, we also derive an error estimate for an asymptotic expansion around a partially elliptic diffusion under a multi-dimensional setting, which includes various important models in finance as the special cases.In particular, we take the Malliavin calculus approach, and estimate the error bounds for the Malliavin weights of both the coefficient and the residual terms in the expansions by effectively applying the properties of Kusuoka-Stroock functions.