Dependence among defaults both across assets and over time has proven to be an important characteristic of financial risk. A Bayesian approach to default rate estimation is proposed and illustrated using a prior distributions assessed from an experienced industry expert. Two extensions of the binomial model, most common in applications, are proposed. The first allows correlated defaults yet remain consistent with Basel II's asymptotic single-factor model. The second adds temporal correlation in default rates through autocorrelation in the systemic factor. Implications for the predictability of default rates are considered. The single-factor model generates more forecast uncertainty than does the parameter uncertainty. A robustness exercise, weakening the prior on the asset correlation, illustrates that the correlation indicated by the data is much smaller than that specified in the Basel II regulations. The application shows that econometric methods can be useful even when data information is sparse.
Bayesian inference Basel II risk management prior elicitation maximum entropy time series