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...

This paper proposes an arbitrary high order weak approximation scheme for multidimensional Stratonovich stochastic differential equations using Malliavin calculus. The scheme efficiently works whether test function is smooth or not. The Malliavin Monte Carlo method, a simple numerical algorithm,...

The paper shows a new weak approximation method for stochastic differential equations as a generalization and an extension of Heath-Platen's scheme for multidimensional diffusion processes. We reformulate the Heath-Platen estimator from the viewpoint of asymptotic expansion. The proposed scheme...