On a Statistical Analysis of Implied Data

We propose a method of evaluating the accuracy of the implied default probabilities. We modify the model proposed by Duffie et al. (Rev Fin Stud 12:678–720, 1999) to allow the parametric statistical analysis. The pseudo maximum likelihood estimator is defined and to justify our method we shall prove the consistency and the asymptotic normality of the estimator. The key step is to define a pseudo score vector and apply the method of Wald (Ann Math Stat 20: 595–601, 1949) and a delta method. We also introduce the bootstrap for estimating the accuracies, which is similar to that for regression models. To implement our method to the real data, we shall recommend the bootstrap rather than asymptotic normality.