Reducing the Variance of Likelihood Ratio Greeks with Monte Carlo

TL;DR

This paper explores variance reduction techniques like Antithetic Variables, Control Variates, and Importance Sampling to improve the accuracy and efficiency of Monte Carlo estimations of option sensitivities, especially for short maturities.

Contribution

It demonstrates how these variance reduction methods effectively address divergence issues and significantly enhance computational efficiency in likelihood ratio-based Greeks estimation.

Findings

Antithetic Variables prevent divergence of Delta variance for short maturities

Control Variates and Importance Sampling yield up to several orders of magnitude in computational savings

Numerical examples within Gaussian Copula framework validate the methods' effectiveness

Abstract

We investigate the use of Antithetic Variables, Control Variates and Importance Sampling to reduce the statistical errors of option sensitivities calculated with the Likelihood Ratio Method in Monte Carlo. We show how Antithetic Variables solve the well-known problem of the divergence of the variance of Delta for short maturities and small volatilities. With numerical examples within a Gaussian Copula framework, we show how simple Control Variates and Importance Sampling strategies provide computational savings up to several orders of magnitude.