Fast Gamma Computations for CDO Tranches

10 Pages Posted: 9 Oct 2010

See all articles by Mark S. Joshi

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Chao Yang

Origin Energy

Date Written: October 8, 2010

Abstract

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

Suggested Citation

Joshi, Mark and Yang, Chao, Fast Gamma Computations for CDO Tranches (October 8, 2010). Available at SSRN: https://ssrn.com/abstract=1689348 or http://dx.doi.org/10.2139/ssrn.1689348

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies (deceased) ( email )

Melbourne, 3010
Australia

Chao Yang

Origin Energy ( email )

Sydney
Australia

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