The paper gives a novel path integral formula inspired by large deviation theory and Malliavin calculus. The proposed finite-dimensional approximation of integrals on path space will be a new higher-order weak approximation of multidimensional stochastic differential equations where the dominant...

This paper proposes a general approximation method for the solution to a second-order parabolic partial differential equation (PDE) widely used in finance through an extension of Leandre's approach (Leandre, 2006, 2008) and the Bismut identiy (e.g. chapter IX-7 of Malliavin, 1997) in Malliavin...

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula in Malliavin calculus is effectively applied in an asymptotic expansion approach. First, the paper derives...

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with...

This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in multi-dimensional stochastic volatility models. In particular, the integration-byparts formula in Malliavin calculus and the push-down of Malliavin...

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach....

Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result....