Graphical models for correlated defaults

TL;DR

This paper introduces a graphical model for correlated defaults that accurately captures default dependence, provides explicit loss distribution formulas, and offers a calibration method, outperforming standard models in tail risk and correlation structures.

Contribution

It presents a novel graphical model for correlated defaults with explicit formulas and a calibration algorithm, enhancing modeling flexibility and accuracy over traditional copula approaches.

Findings

Model accurately captures default dependence

Provides explicit formulas for loss distribution

Outperforms normal copula in tail risk and correlation smile

Abstract

A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given marginal distribution for single firms and pairwise correlation matrix. These techniques also provide a calibration algorithm based on maximum likelihood estimation. Finally, the model is compared with standard normal copula model in terms of tails of the loss distribution and implied correlation smile.