Random survival forests and Cox regression in loss given default estimation

Aneta Ptak-Chmielewska and Paweł Kopciuszewski

Abstract

Banks that apply the advanced internal ratings-based approach rely on their own data in the estimation of risk parameters such as probability of default, exposure at default and loss given default (LGD). However, in some portfolios, such as mortgage portfolios, the number of observed defaults is always very small. The issue of small samples in LGD estimation is always a challenge for researchers. In this paper we propose a basic LGD model based on the survival approach, implemented as a Cox semiparametric model and as a random survival forest. The main contribution of this paper, however, is that it addresses unresolved cases incorporated in the LGD estimation process by using the survival approach, which assumes the censoring of unresolved cases. Traditional methods used in previous studies on applied LGD estimation tend not to include the survival approach. The most common approaches involve regression modeling or ensemble methods. An additional contribution of this paper is that the proposed modeling approach for LGD is illustrated with real data on mortgages of a European bank.