Reducing the Variance of Likelihood Ratio Greeks with Monte Carlo

Details Reducing the Variance of Likelihood Ratio Greeks with Monte Carlo Reducing the Variance of Likelihood Ratio Greeks with Monte Carlo

2008-08-18

arxiv.org/abs/0808.2332v1

Physics

Data Analysis, Statistics and Probability

4 pages, 2 figures

Scientific paper

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.

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