We show a new higher order weak approximation with Malliavin weights for multidimensional stochastic differential equations by extending the method in Takahashi and Yamada (2016). The estimate of global error of the discretization is based on a sharp small time expansion using a Malliavin...

This paper presents a mathematical validity for an asymptotic expansion scheme of the solutions to the forward-backward stochastic differential equations (FBSDEs) in terms of a perturbed driver in the BSDE and a small diffusion in the FSDE. This computational scheme was proposed by...

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 introduces a new efficient and practical weak approximation for option price under local stochastic volatility model as marginal expectation of stochastic differential equation, using iterative asymptotic expansion with Malliavin weights. The explicit Malliavin weights for SABR model...

This paper proposes a general higher order operator splitting scheme for diffusion semigroups using the Baker-Campbell-Hausdorff type commutator expansion of non-commutative algebra and the Malliavin calculus. An accurate discretization method for the fundamental solution of heat equations or...

The paper proposes a new automatic/algorithmic differentiation for the solutions to partial differential equations of parabolic type. In particular, we provide a higher order discretization scheme which is a natural extension of the standard automatic differentiation. A Brownian polynomial...

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...

This paper proposes a new third-order discretization algorithm for multidimensional Itô stochastic differential equations driven by Brownian motions. The scheme is constructed by the Euler-Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply...