The two defaults scenario for stressing credit portfolio loss distributions

TL;DR

This paper develops an analytical method to evaluate the impact of default stress scenarios on credit portfolio loss distributions, especially for multiple defaults, and compares it to Monte Carlo simulations.

Contribution

It introduces an analytical approach for conditional loss distribution calculation in the CreditRisk+ model, improving accuracy over traditional Monte Carlo methods for stressed defaults.

Findings

The analytical solution is unbiased compared to simulation.

The approximation tends to overestimate tail losses, providing a conservative estimate.

Numerical examples demonstrate the method's effectiveness and limitations.

Abstract

The impact of a stress scenario of default events on the loss distribution of a credit portfolio can be assessed by determining the loss distribution conditional on these events. While it is conceptually easy to estimate loss distributions conditional on default events by means of Monte Carlo simulation, it becomes impractical for two or more simultaneous defaults as then the conditioning event is extremely rare. We provide an analytical approach to the calculation of the conditional loss distribution for the CreditRisk+ portfolio model with independent random loss given default distributions. The analytical solution for this case can be used to check the accuracy of an approximation to the conditional loss distribution whereby the unconditional model is run with stressed input probabilities of default (PDs). It turns out that this approximation is unbiased. Numerical examples, however, suggest that the approximation may be seriously inaccurate but that the inaccuracy leads to overestimation of tail losses and hence the approach errs on the conservative side.