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 Bernoulli-type random variables Si (i = 1,иии,N). They are expressed by multiplying independent Bernoulli variables Xi , Yij and Y′ij , and the default and recovery infections are described by Yij 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 Si ↔ 1 − Si . 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.
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. 054801-054807.