Second Order Discretization of Bismut-Elworthy-Li Formula: Application to Sensitivity Analysis
SIAM/ASA Journal on Uncertainty Quantification, 2018
Posted: 12 Feb 2019
Date Written: November 28, 2018
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
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