A Second Order Discretization with Malliavin Weight and Quasi-Monte Carlo Method for Option Pricing

Abstract

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 simulation is proposed to attain an efficient option pricing scheme. Numerical examples for the SABR model are shown to illustrate the validity of the scheme.