Infectious Default Model with Recovery and Continuous Limits

Abstract

We introduce an infectious default and recovery model for N obligors. The obligors are assumed to be exchangeable and their states are described by N Bernoulli-type random variables S_i (i=1,…,N). They are expressed by multiplying independent Bernoulli variables X_i, Y_ij, and Y′_ij, and the default and recovery infections are described by Y_ij and Y′_ij. We obtain the default probability function P(k) for k defaults. By considering a continuous limit, we find two nontrivial probability distributions with a reflection symmetry of S_i↔1−S_i. Their profiles are singular and oscillating and we theoretically investigate it. We also compare P(k) with an implied default distribution function inferred from the quotes of iTraxx-CJ, which is a portfolio credit derivative of Japanese 50 companies. In order to explain the behavior of the implied distribution, the recovery effect may be necessary.