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Finance and Stochastics

, Volume 13, Issue 4, pp 613–633

First Online: 11 July 2009Received: 24 January 2008Accepted: 12 January 2009


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.

KeywordsInteracting particle systems Rare defaults Monte Carlo methods Credit derivatives Variance reduction Mathematics Subject Classification 200060H35 91B70 JEL ClassificationC63  Download to read the full article text

Autor: René Carmona - Jean-Pierre Fouque - Douglas Vestal


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