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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Carmona, R., Fouque, JP. & Vestal, D. Interacting particle systems for the computation of rare credit portfolio losses. Finance Stoch 13, 613–633 (2009). https://doi.org/10.1007/s00780-009-0098-8
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DOI: https://doi.org/10.1007/s00780-009-0098-8