A Second Order Discretization with Malliavin Weight and Quasi-Monte Carlo Method for Option Pricing
22 Pages Posted: 7 Aug 2017 Last revised: 6 Feb 2018
Date Written: February 6, 2018
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.
Keywords: option pricing, European option, digital option, Quasi Monte Carlo method, SABR model, weak approximation, stochastic differential equations, Malliavin calculus
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