This master’s thesis deals with nonparametric methods from survival analysis based on kernel smoothing and their applications to Credit Risk. With Beran’s estimator as the starting point, we give a self-contained account of the current research on this topic, focusing in particular on cure models and the NPCM estimator (“nonparametric cure model”) as well as a semiparametric dimension reduction technique. Detailed proofs of many theoretical results are presented in a fashion accessible to readers with limited previous knowledge on the topic. Our main references for this are Pel´aez et al. (2022a) and Li and Patilea (2018). In addition to this discussion of the state of the art, the research contribution of this thesis is two-fold. First, we consider a parameter-free technique to smooth estimated survival curves with respect to time that is based on B´ezier-curves and compare it to a kernel smoothing approach that is commonly used. Secondly, we propose to use the NPCM estimator to estimate recovery rates in the context of Credit Risk. We argue that cure models can be well-suited for the bathtub shape commonly observed in recovery rate distributions. Applying the NPCM estimator and a single-index dimension reduction technique to a data set of defaulted peer-to-peer loan exposures, we find that this model — while using fewer risk factors — can produce results that are competitive with a benchmark linear regression model obtained by stepwise selection.     «

This master’s thesis deals with nonparametric methods from survival analysis based on kernel smoothing and their applications to Credit Risk. With Beran’s estimator as the starting point, we give a self-contained account of the current research on this topic, focusing in particular on cure models and the NPCM estimator (“nonparametric cure model”) as well as a semiparametric dimension reduction technique. Detailed proofs of many theoretical results are presented in a fashion accessible to reader...     »