Interacting Particle Systems for the Computation of CDO Tranche Spread with Rare Defaults

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Interacting Particle Systems for the Computation of CDO Tranche Spread with Rare Defaults

by Douglas Vestal of the University of California, Santa Barbara,
René Carmona of Princeton University, and
Jean-Pierre Fouque of the
University of California, Santa Barbara

January 24, 2008

Abstract: We propose an Interacting Particle System method to accurately calculate the distribution of the losses in a highly dimensional portfolio by using a selection and mutation algorithm. We demonstrate the efficiency of this method for computing rare default probabilities on a toy model for which we have explicit formulas. This method has the advantage of accurately computing small probabilities without requiring the user to compute a change of measure as in the Importance Sampling method. This method will be useful for computing the senior tranche spreads in Collateralized Debt Obligations (CDOs).

Keywords: Interacting Particle Systems, Rare Defaults, Monte Carlo Methods, Credit Derivatives, Variance Reduction.

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