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Interacting Particle Systems for the Computation of Rare Credit Portfolio Losses

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

September 2009

Abstract: In this paper, we introduce the use of interacting particle systems in the computation of probabilities of simultaneous defaults in large credit portfolios. The method can be applied to compute small historical as well as risk-neutral probabilities. It only requires that the model be based on a background Markov chain for which a simulation algorithm is available. We use the strategy developed by Del Moral and Garnier in (Ann. Appl. Probab. 15:2496-2534, 2005) for the estimation of random walk rare events probabilities. For the purpose of illustration, we consider a discrete time version of a first passage model for default. We use a structural model with stochastic volatility, and we demonstrate the efficiency of our method in situations where importance sampling is not possible or numerically unstable.

JEL Classification: C63.

AMS Classification: 60H35, 91B70.

Keywords: Interacting particle systems, Rare defaults, Monte Carlo methods, Credit derivatives, Variance reduction.

Published in: Finance and Stochastics, Vol. 13, No. 4, (September 2009), pp. 613-633.

Previously titled: Interacting Particle Systems for the Computation of CDO Tranche Spreads with Rare Defaults

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Related reading: Exact and Efficient Simulation of Correlated Defaults