Joint Default Probabilities: A Model with Time-varying and Correlated Sharpe Ratios and Volatilities

Abstract

The probabilities of joint default among companies are one of the major concerns in credit risk management, mainly because it aects the distribution of loan portfolio losses and is therefore critical when allocating capital for solvency purposes. This paper proposes a multivariate model with time-varying and correlated Sharpe ratios and volatilities for the value of the rms, calibrated to t sample averages between and within the rating categories A and Ba. We found that, in the standard Merton framework, the model performs well with one average A-rated rm and one average Ba-rated rm and with two average Ba-rated rms when the joint default probabilities are compared with similar empirical probabilities.