Journal of Risk Model Validation

A correlated structural credit risk model with random coefficients and its Bayesian estimation using stock and credit market information

Tae Yeon Kwon

  • Under Black-Cox structural setups, this paper proposes a correlated defaults model that enables the use of equity prices and credit spreads at the same time in model estimation.
  • We estimate the model across the 125 issuers that make up the CDX index, using a modified generalized Gibbs sampling scheme.
  • The correlation of defaults is modelled using the assumption that asset value processes depend on the common factors (market return and value premium) but can differ in their degree of dependence on them.
  • The results of our simulation studies show that our estimation method makes posterior chains converge more quickly to the true values when both stock prices and CDS spreads are used than with stock prices alone.


Using historical equity and credit market data, we illustrate the validation of a structural correlated default model applied to Black-Cox setups. We model the dependence structure through the imposition of common factors on the asset process. Instead of assuming homogeneity in the effects of the common factor across the firms, we consider a random coefficient representing the heterogeneity effect. Based on the Bayesian method, we estimate model parameters using not only equity prices but also credit default swap (CDS) spreads. Through our simulation studies, we found that the estimation performance improved when both stock prices and CDS spreads were used compared with the use of stock prices alone. Our empirical analysis is based on daily data for the 125 issuers comprising the CDS.NA.IG13 in 2009. In order to demonstrate potential practical applications and check the out-of-sample model validation, we derive the posterior distribution of CDX tranche prices.

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