This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate...

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,...

This paper shows an efficient second order discretization scheme of expectations of stochastic differential equations. We introduce smart Malliavin weight which is given by a simple polynomials of Brownian motions as an improvement of the scheme of Yamada (2017). A new quasi Monte Carlo...