Sample-path Large Deviations in Credit Risk

TL;DR

This paper develops a large deviation framework for analyzing rare, large losses in credit risk portfolios, providing tools to compute the decay rates of tail probabilities and exact asymptotics for specific events.

Contribution

It introduces a sample-path large deviation principle for the loss process, enabling precise analysis of rare loss events in credit portfolios.

Findings

Derived a sample-path large deviation principle for the loss process

Provided exact asymptotics for specific rare-event probabilities

Enabled computation of decay rates for tail risk in credit portfolios

Abstract

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail asymptotics of the probabilities involved. We first derive a sample-path large deviation principle (LDP) for the portfolio's loss process, which enables the computation of the logarithmic decay rate of the probabilities of interest. In addition, we derive exact asymptotic results for a number of specific rare-event probabilities, such as the probability of the loss process exceeding some given function.