A la Carte of Correlation Models: Which One to Choose?

TL;DR

This paper introduces a flexible copula contagion mixture model for correlated defaults, enabling analysis of various models' interactions and their effects on pricing complex credit derivatives.

Contribution

It develops a unified framework that encompasses factor, copula, and contagion models, allowing for comparative analysis of their pricing impacts.

Findings

The model captures diverse default dependence structures.

Pricing differences are significant across models.

Numerical comparisons highlight model-specific effects on basket CDSs and CDOs.

Abstract

In this paper we propose a copula contagion mixture model for correlated default times. The model includes the well known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the marginal default times to follow some contagion intensity processes coupled with copula dependence structure. We apply the total hazard construction method to generate ordered default times and numerically compare the pricing impact of different models on basket CDSs and CDOs in the presence of exponential decay and counterparty risk.