How to Estimate Default Intensity Processes
This chapter presents the theory underlying the maximum likelihood estimation of term structures of survival probabilities, for example the dependence of default probability on time horizon. The methodology allows the events of concern to be censored by disappearance of corporations from the data, due for instance to merger or acquisition. The idea is to estimate the parameter vector determining the default intensity as well as the parameter vector determining the transition probabilities of the covariate process, and then to use the maximum likelihood estimator of these parameters to estimate the survival probabilities of the corporations, for a range of choices of the survival horizon. The results show that the joint estimation of the parameters is relatively tractable under the doubly-stochastic property.
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