Inferring the Default Rate in a Population by Comparing Two Incomplete Default Databases
by Douglas W. Dwyer of Moody's|KMV, and
Abstract: It is often the case in default modeling that the need arises to calibrate a model to some prior probability of default. In many situations, a researcher may not know the true prior default rate for the population because the data set at hand is itself incomplete either with respect to default identification (hidden defaults) or default under reporting. In situations where a researcher has access to two incomplete default data sets, it is possible to infer the number of "missing" defaults, which we demonstrate in this short note. We discuss an approach to estimating this quantity and show an example in which we infer the number of missing defaults in the combined legacy databases of the former Moody's Risk Management Services and KMV. While calibration is one application of this approach, the method is quite general and can be applied in other settings as well.
Published in: Journal of Banking & Finance, Vol. 30, No. 3, (March 2006), pp. 797-810.