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...

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 a general approximation method for the solutions to second order parabolic partial differential equations (PDEs) by an extension of Leandre's approach and the Bismut identity in Malliavin calculus. We show two types of its applications, new approximations of derivatives...

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...