Computing worst-case tail probabilities in credit risk
Proceedings of the 38th conference on Winter simulation
Conditional Monte Carlo Estimation of Quantile Sensitivities
Management Science
Original Articles: t-Copula generation for control variates
Mathematics and Computers in Simulation
Exact and Efficient Simulation of Correlated Defaults
SIAM Journal on Financial Mathematics
Improved cross-entropy method for estimation
Statistics and Computing
Markov chain importance sampling with applications to rare event probability estimation
Statistics and Computing
Iimportance sampling for risk contributions of credit portfolios
Proceedings of the Winter Simulation Conference
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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.