Portfolio credit risk with extremal dependence: Asymptotic analysis and efficient simulation

Achal Bassamboo*, Sandeep Juneja, Assaf Zeevi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


We consider the risk of a portfolio comprising loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in performance measures such as the probability that the portfolio incurs large losses over a fixed time horizon, and the expected excess loss given that large losses are incurred during this horizon. Contrary to the normal copula that is commonly used in practice (e.g., in the CreditMetrics system), we assume a portfolio dependence structure that is semiparametric, does not hinge solely on correlation, and supports extremal dependence among obligors. A particular instance within the proposed class of models is the so-called, t-copula model that is derived from the multivariate Student t distribution and hence generalizes the normal copula model. The size of the portfolio, the heterogeneous mix of obligors, and the fact that default events are rare and mutually dependent make it quite complicated to calculate portfolio credit risk either by means of exact analysis or naïve Monte Carlo simulation. The main contributions of this paper are twofold. We first derive sharp asymptotics for portfolio credit risk that illustrate the implications of extremal dependence among obligors. Using this as a stepping stone, we develop importance-sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.

Original languageEnglish (US)
Pages (from-to)593-606
Number of pages14
JournalOperations Research
Issue number3
StatePublished - May 2008


  • Asymptotics
  • Credit
  • Expected shortfall
  • Importance sampling
  • Portfolio
  • Rare events
  • Risk management
  • Simulation

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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