Statistical Methods in Credit Risk Modeling.

Abstract

This research deals with some statistical modeling problems that are motivated by credit risk analysis. Credit risk modeling has been the subject of considerable research interest in finance and has recently drawn the attention of statistical researchers. In the first chapter, we provide an up-to-date review of credit risk models and demonstrate their close connection to survival analysis.

The first statistical problem considered is the development of adaptive smoothing spline (AdaSS) for heterogeneously smooth function estimation. Two challenging issues that arise in this context are evaluation of reproducing kernel and determination of local penalty, for which we derive an explicit solution based on piecewise type of local adaptation. Our nonparametric AdaSS technique is capable of fitting a diverse set of `smooth' functions including possible jumps, and it plays a key role in subsequent work in the thesis.

The second topic is the development of dual-time analytics for observations involving both lifetime and calendar timescale. It includes "vintage data analysis" (VDA) for continuous type of responses in the third chapter, and "dual-time survival analysis" (DtSA) in the fourth chapter. We propose a maturation-exogenous-vintage (MEV) decomposition strategy in order to understand the risk determinants in terms of self-maturation in lifetime, exogenous influence by macroeconomic conditions, and heterogeneity induced from vintage originations. The intrinsic identification problem is discussed for both VDA and DtSA. Specifically, we consider VDA under Gaussian process models, provide an efficient MEV backfitting algorithm and assess its performance with both simulation and real examples.

DtSA on Lexis diagram is of particular importance in credit risk modeling where the default events could be triggered by both endogenous and exogenous hazards. We consider nonparametric estimators, first-passage-time parameterization and semiparametric Cox regression. These developments extend the family of models for both credit risk modeling and survival analysis. We demonstrate the application of DtSA to credit card and mortgage risk analysis in retail banking, and shed some light on understanding the ongoing credit crisis.