Fast Gamma Computations for CDO Tranches
10 Pages Posted: 9 Oct 2010
Date Written: October 8, 2010
We demonstrate how to compute first- and second-order sensitivities of portfolio credit derivatives such as synthetic collateralized debt obligation (CDO) tranches using algorithmic Hessian methods developed in Joshi and Yang (2010) in a single-factor Gaussian copula model. Our method is correct up to floating point error and extremely fast. Numerical result shows that, for an equity tranche of a synthetic CDO with 125 names, we are able to compute the whole Gamma matrix with computational times measured in seconds.
Keywords: portfolio credit derivatives, copula modelling, semi-analytic method, algorithmic differentiation
JEL Classification: G13
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