Default Correlation: The Basics

The Journal of Fixed Income, 2006

Fixed-Income portfolios are increasingly susceptible to correlated default risk. Defaults of individual firms will cluster if there are common factors that affect each firm's default risk. Using a comprehensive dataset of firm-level default probabilities, we examine co-variation of default probabilities across US public non-financial firms. We observe that systematic time-variation in default risk is driven more by an economy-wide volatility factor than by changing debt levels, and therefore is closely linked to the business cycle. Specifically, both default probabilities and default correlations vary over time resulting in substantial variation in joint default risk. For example, over the latter half of the 1990s, default probabilities across the economy doubled, and correlations increased by an even greater magnitude. We provide a reduced-form framework to jointly model time variation in both default probabilities and their correlations over the business cycle. Calibration of the model demonstrates the economic importance of modeling time-variation of joint default risk; for example, our model suggests that the ex-ante probability of observing the record defaults of 2001 doubled across regimes. We also document cross-sectional differences across rating classes-default probability correlations are higher amongst higher quality issuers.

2000

Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity’s diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of “diversifiable default risk.” The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999). We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgage-backed securities. Reduced-form models of defaultable secur...

2008

2007

Abstract The characterization of the default dependence across different firms is a central problem in the credit risk literature. The valuation of structured credit products such as collateralized debt obligation (CDOs) tranches critically depend on this dependence structure. We use a two-step procedure to characterize the time variation in the correlation structure of default probabilities. In a first stage, default intensities are filtered from credit default swap (CDS) contracts using a reduced form model.

This work incorporates issuer default risk into basket credit linked note (BCLN) pricing. Under the standard market model of the one factor Gaussian copula, the effect of issuer default risk on the fair BCLN coupon rate is discussed. The analysis results demonstrate that issuer default risk increases the fair coupon rate. However, contradicting the common conception that a negative default correlation between the reference entities and the issuer reduces the possibility of double loss and favors the BCLN holder, thus reducing BCLN coupon rate, the analysis results reveal that the negative default correlation disfavors the BCLN holder. Furthermore, the coupon rate increases as the default correlation approaches negative one. The proposed framework effectively reflects issuer default risk in the fair BCLN coupon rate.

Finance Research Letters, 2018

We empirically test the theoretical prediction of the impact of debt market liquidity on correlated default risk. Confirming the theory, our results indicate that the lower debt market liquidity, leads to an economically significant increase in the correlated default risk. Also consistent with theory, we show that this effect is more pronounced for short-term debt.

2006

We study the pricing of collateralized debt obligations (CDOs) using an extensive new data set for the actively-traded CDX credit index and its tranches. We find that a three-factor portfolio credit model allowing for rm-speci c, industry, and economywide default events explains virtually all of the time-series and crosssectional variation in CDX index tranche prices. These tranches are priced as if losses of 0.4, 6, and 35 percent of the portfolio occur with expected frequencies of 1.2, 41.5, and 763 years, respectively. On average, 65 percent of the CDX spread is due to firm-specific default risk, 27 percent to clustered industry or sector default risk, and 8 percent to catastrophic or systemic default risk. Recently, however, firm-specific default risk has begun to play a larger role.

Mathematical Finance, 2005

Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity's diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of "diversifiable default risk." The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999). We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgage-backed securities.

2016

Implementation of reliable rating systems for small credit portfolio is hindered by non-observed default events in databases and short time series of data available. In this study we propose an approach to handle those two challenges while developing rating systems. We further extend the approach by estimating systematic risk, that is, co-movements of creditworthiness of debt securities' issuers over time. Based on financial information from the PSVaG's debt securities portfolio, we could show that including a systematic risk component significantly increase the model accuracy.

SSRN Electronic Journal, 2014

Central bank lending to commercial banks is typically collateralized which reduces central bank's credit risk exposure to "double default events" when the counterparty and the issuer of the underlying collateral asset both default in a short period of time. This paper presents a simple model for correlated defaults which are the key drivers of residual credit risk in central bank's repo portfolios. In the model default times of counterparties and collateral issuers are determined by idiosyncratic and systematic factors, whereby a name defaults if it is struck by either factor for the first time. The novelty of our approach lies in representing systematic factors as increasing sequences of random variables. Such a setting allows to build a rich dependence structure that is free of the flaws inherent in the Gaussian copula-based approaches currently regarded as state of the art solutions for central banks.