Estimating the Term Structure of Default Probabilities for Heterogeneous Credit Porfolios

Abstract: The aim of this thesis is to estimate the term structure of default probabilities for heterogeneous credit portfolios. The term structure is defined as the cumulative distribution function (CDF) of the time until default. Since the CDF is the complement of the survival function, survival analysis is applied to estimate the term structures. To manage long-term survivors and plateaued survival functions, the data is assumed to follow a parametric as well as a semi-parametric mixture cure model. Due to the general intractability of the maximum likelihood of mixture models, the parameters are estimated by the EM algorithm. A simulation study is conducted to assess the accuracy of the EM algorithm applied to the parametric mixture cure model with data characterized by a low default incidence. The simulation study recognizes difficulties in estimating the parameters when the data is not gathered over a sufficiently long observational window. The estimated term structures are compared to empirical term structures, determined by the Kaplan-Meier estimator. The results indicated a good fit of the model for longer horizons when applied to each credit type separately, despite difficulties capturing the dynamics of the term structure for the first one to two years. Both models performed poorly with few defaults. The parametric model did however not seem sensitive to low default rates. In conclusion, the class of mixture cure models are indeed viable for estimating the term structure of default probabilities for heterogeneous credit portfolios.