Worst - Case Tail Probabilities in Credit Risk

Simulation is widely used to measure credit risk in portfolios of loans, bonds, and other instruments subject to possible default. This analysis requires performing the difficult modeling task of capturing the dependence between obligors adequately. Current methods assume a form for the joint distribution of the obligors and match its parameters to given dependence specifications, usually correlations. The value-at-risk risk measure (a function of its tail quantiles) is then evaluated. This procedure is naturally limited by the form assumed, and might not approximate well the “worstcase” possible over all joint distributions that match the given specification. We propose a procedure that approximates the joint distribution with chessboard distributions, and provides a sequence of improving estimates that asymptotically approach this “worst-case” value-at-risk. We use it to experimentally compare the quality of the estimates provided by the earlier procedures.