
 Infectious Default Model with Recovery and Continuous Limits by Ayaka Sakata of the University of Tokyo, January 20, 2008 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 Bernoullitype 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 iTraxxCJ, 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. Keywords: default correlation, correlated binomial, default distribution, continuous limit. Published in: Journal of the Physical Society of Japan, Vol. 76, No. 5, (May 2007), pp. 054801054807. Books Referenced in this paper: (what is this?) 