Fast Correlation Greeks by Adjoint Algorithmic Differentiation
AbstractWe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1004.1855.
Date of creation: Apr 2010
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Publication status: Published in Risk Magazine, April 2010
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-24 (All new papers)
- NEP-CMP-2010-04-24 (Computational Economics)
- NEP-RMG-2010-04-24 (Risk Management)
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- Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.
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