State dependent correlations in the Vasicek default model

Abstract

This paper incorporates state dependent correlations (those that vary systematically with the state of the economy) into the Vasicek default model. Other approaches to randomizing correlation in the Vasicek model have either assumed that correlation is independent of the systematic risk factor (zero state dependence) or is an explicit function of the systematic risk factor (perfect state dependence). By contrast, our approach allows for an arbitrary degree of state dependence and includes both zero and perfect state dependence as special cases. This is accomplished by expressing the factor loading as a function of an auxiliary (Gaussian) variable that is correlated with the systematic risk factor. Using Federal Reserve data on delinquency rates we use maximum likelihood to estimate the parameters of the model, and find the empirical degree of state dependence to be quite high (but generally not perfect). We also find that randomizing correlation, without allowing for state dependence, does not improve the empirical performance of the Vasicek model.

Keywords

• one-factor gaussian copula
• vasicek model
• stochastic correlation
• regulatory capital
• 60e99
• 62e99