Dynamic Portfolio Credit Risk and Large Deviations

Abstract

We consider a multi-time period portfolio credit risk model. The default probabilities of each obligor in each time period depend upon common as well as firm specific factors. The time movement of these factors is modelled as a vector autoregressive process. The conditional default probabilities are modelled using a general representation that subsumes popular default intensity models, logit-based models as well as threshold based Gaussian copula models. We develop an asymptotic regime where the portfolio size increases to infinity. In this regime, we conduct large deviations analysis of the portfolio losses. Specifically, we observe that the associated large deviations rate function is a solution to a quadratic program with linear constraints. Importantly, this rate function is independent of the specific modelling structure of conditional default probabilities. This rate function may be useful in identifying and controlling the underlying factors that contribute to large losses, as well as in designing fast simulation techniques for efficiently measuring portfolio tail risk.