Fast Correlation Greeks by Adjoint Algorithmic Differentiation

6 Pages Posted: 12 Apr 2010

See all articles by Luca Capriotti

Luca Capriotti

Columbia University

Michael B. Giles

University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: April 11, 2010

Abstract

We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illustrate the method for a copula-based Monte Carlo computation of claims written on a basket of underlying assets, and we test it numerically for Portfolio Default Options. For any number of underlying assets or names in a portfolio, the sensitivities of the option price with respect to all the pairwise correlations is obtained at a computational cost which is at most 4 times the cost of calculating the option value itself. For typical applications, this results in computational savings of several order of magnitudes with respect to standard methods.

Keywords: Algorithmic Differentiation, Monte Carlo Simulations, Derivatives Pricing, Credit Derivatives

Suggested Citation

Capriotti, Luca and Giles, Michael B., Fast Correlation Greeks by Adjoint Algorithmic Differentiation (April 11, 2010). Available at SSRN: https://ssrn.com/abstract=1587822 or http://dx.doi.org/10.2139/ssrn.1587822

Luca Capriotti (Contact Author)

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Michael B. Giles

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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