Credit Risk Modeling Using Excel and VBA with DVD

6

Modeling and Estimating Default Correlations with the Asset Value Approach

The previous chapters have focused on the measurement of individual default probabilities. For a financial institution that wants to assess the default risk of its loan portfolio, however, individual default probabilities are not enough. Consider the simplest case: a portfolio comprises only two borrowers, and the bank would like to know the probability that both borrowers default in the next period. This cannot be measured with the default probabilities alone. We could assume that the two borrowers are independent. The probability that both of them default would then equal the product of the two individual default probabilities. Default rates of firms, however, fluctuate with macroeconomic or industry-specific conditions, and so we should not rely on defaults being independent.

What we need to know in this case is the joint default probability. As we see in this chapter, this will lead us directly to the default correlation. We also examine a widely used way of modeling default correlations, the so-called asset value approach. We show how to estimate the relevant parameters based on historical default experience and how to assess the quality of the parameter estimates. The two estimation methods that we consider are the method of moments approach and the maximum likelihood approach.

DEFAULT CORRELATION, JOINT DEFAULT PROBABILITIES AND THE ASSET VALUE APPROACH

To formalize default correlation, we use the ...