On an Infectious Model for Default Crisis

In this paper, we look at the problem of modelling the temporal dependence of defaults and introduce a novel approach for describing the chain reaction of infectious defaults. We extend a Markov chain model for crisis management in epidemiology, namely, Greenwood's model, to describe the chain reaction of infectious defaults of bonds across any pair of industrial sectors. The development of the extended version of Greenwood's model contributes to the literature in two major aspects. First, it contributes to the credit risk literature by providing a new framework for measuring risk of a credit portfolio over the duration of a default crisis, called a default cycle. This is different from the traditional approach for risk measurement in which the time horizon is fixed, say one day or one week, and leads to a new dimension for risk management. Second, it provides a new model for crisis management in epidemiology by extending an important model in the field. We employ recursive formulae for the joint probability distributions of the duration of a default crisis and the number of defaults over the crisis. Moreover, we employ two important risk measures, namely, Value-at-Risk (VaR) and Expected Shortfall (ES), as proxies of risk over a default cycle. Numerical experiments are given to illustrate the practical implementation of the model and identify some main features of the model. We also perform empirical studies of the model using real default data and analyze the empirical behaviors of the risk measures arising from the model.