Default clustering in large portfolios: Typical events

TL;DR

This paper introduces a dynamic point process model for correlated defaults in large portfolios, analyzing typical default patterns as the portfolio size increases, with implications for risk management.

Contribution

It develops a novel stochastic intensity model incorporating systemic, idiosyncratic, and default history effects, and proves a law of large numbers for default rates.

Findings

Law of large numbers for default rate established

Model captures systemic and default history influences

Describes typical default behavior in large portfolios

Abstract

We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to all firms, and past defaults. We prove a law of large numbers for the default rate in the pool, which describes the "typical" behavior of defaults.