Second Order Discretization of Bismut-Elworthy-Li Formula: Application to Sensitivity Analysis

SIAM/ASA Journal on Uncertainty Quantification, 2018

Posted: 12 Feb 2019

See all articles by Toshihiro Yamada

Toshihiro Yamada

Hitotsubashi University

Kenta Yamamoto

Bank of Tokyo-Mitsubishi, Ltd.

Date Written: November 28, 2018

Abstract

This paper shows a higher order discretization scheme for the Bismut-Elworthy-Li formula, the differentiation of diffusion semigroups. A weak approximation type algorithm with Malliavin weights is constructed through the integration by parts on Wiener space and is efficiently implemented by a Monte Carlo method. We give a sharp error estimate for the discretization based on Malliavin calculus. Numerical sensitivity analysis for the option delta in finance shows the validity of the proposed scheme.

Keywords: Bismut-Elworthy-Li Formula, Stochastic Differential Equations, Weak Approximation, Sensitivity Analysis, Malliavin Calculus, Monte Carlo Simulation

Suggested Citation

Yamada, Toshihiro and Yamamoto, Kenta, Second Order Discretization of Bismut-Elworthy-Li Formula: Application to Sensitivity Analysis (November 28, 2018). SIAM/ASA Journal on Uncertainty Quantification, 2018. Available at SSRN: https://ssrn.com/abstract=3326759

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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