The Underlying Dynamics of Credit Correlations

TL;DR

This paper introduces a hybrid credit risk model using a one-factor GARCH process, highlighting how asymmetric TARCH volatility captures persistent credit correlation skews affecting CDO tranche pricing and risk management.

Contribution

It develops a new correlation surface tool and demonstrates that asymmetric TARCH models effectively generate realistic credit correlation skews over long horizons.

Findings

Asymmetric TARCH models produce significant credit correlation skews.

Correlation skew depends on maturity and hazard rate.

The model impacts CDO tranche valuation and risk management.

Abstract

We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation surface as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews. The characteristic dependence of the correlation skew on term to maturity and portfolio hazard rate in these models has a significant impact on both relative value analysis and risk management of CDO tranches.