Dual-frailty default intensity model: estimations and an application

Abstract

In this paper, a new default intensity model with dual frailties is proposed and an empirical evidence is provided to confirm the model’s adequacy. In addition to the conventional explanatory variables, Duffie et al. introduces a time frailty and Chava et al. considers an industrial frailty to model the conditional default dependence. However, from an empirical study on Taiwan’s public listed firms, Lin and Chen points out that the time frailty can only catch the default dependence along the time but not among the industries. On the other hand, the industrial frailty can only capture the default dependence from the industrial correlation but not from the time dependence. Hence, the default intensity model with time and industrial frailties is recommended. This paper introduces a dual frailty model to incorporate time and industrial frailties. Using the empirical data of Taiwan’s public listed firms from January of 1995 to January of 2015, the dual frailty model is estimated and the Fisher’s dispersion tests are conducted for bins from time and from industries. Our empirical findings indicate that the dual frailty model captures not only the time dependence of default clustering but also the industrial correlations. Therefore, our dual frailty model outperforms the intensity model with time frailty of Duffie et al. and the industrial frailty of Chava et al.