Correlated defaults, temporal correlation, expert information and predictability of default rates

ABSTRACT

Dependence among defaults both across assets and over time is an important characteristic of financial risk. A Bayesian approach to default rate estimation is proposed and illustrated using prior distributions assessed from an experienced industry expert. Two extensions of the binomial model are proposed. The first allows correlated defaults yet remains 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 illustrates that the correlation indicated by the data is much smaller than that specified in the Basel II regulations.

KEYWORDS:

• Basel II
• Bayesian inference
• maximum entropy
• prior elicitation
• risk management
• time series

JEL CLASSIFICATION:

• C11
• C53
• C22
• G17
• G18
• G21