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Fast Correlation Greeks by Adjoint Algorithmic Differentiation

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  • Luca Capriotti
  • Mike Giles

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.

Suggested Citation

  • Luca Capriotti & Mike Giles, 2010. "Fast Correlation Greeks by Adjoint Algorithmic Differentiation," Papers 1004.1855, arXiv.org.
  • Handle: RePEc:arx:papers:1004.1855
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    File URL: http://arxiv.org/pdf/1004.1855
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    Cited by:

    1. Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.
    2. repec:eee:apmaco:v:269:y:2015:i:c:p:412-431 is not listed on IDEAS

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