Interacting particle systems for the computation of rare credit portfolio losses

Rene A. Carmona, Jean Pierre Fouque, Douglas Vestal

Research output: Contribution to journalArticle

32 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)613-633
Number of pages21
JournalFinance and Stochastics
Volume13
Issue number4
DOIs
StatePublished - Jul 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

Keywords

  • Credit derivatives
  • Interacting particle systems
  • Monte Carlo methods
  • Rare defaults
  • Variance reduction

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