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

See all articles by Toshihiro Yamada

Toshihiro Yamada

Hitotsubashi University

Kenta Yamamoto

Bank of Tokyo-Mitsubishi, Ltd.

Date Written: February 6, 2018

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.

Keywords: option pricing, European option, digital option, Quasi Monte Carlo method, SABR model, weak approximation, stochastic differential equations, Malliavin calculus

Suggested Citation

Yamada, Toshihiro and Yamamoto, Kenta, A Second Order Discretization with Malliavin Weight and Quasi-Monte Carlo Method for Option Pricing (February 6, 2018). Available at SSRN: https://ssrn.com/abstract=3012898 or http://dx.doi.org/10.2139/ssrn.3012898

Toshihiro Yamada (Contact Author)

Hitotsubashi University ( email )

2-1 Naka Kunitachi-shi
Tokyo 186-8601
Japan

Kenta Yamamoto

Bank of Tokyo-Mitsubishi, Ltd. ( email )

Japan

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