Default Distribution and Credit Market Implications

by Shintaro Mori of Kitasato University,
Kenji Kitsukawa of Keio University, and
Masato Hisakado of Standard and Poor's

September 18, 2007

Abstract: We study the implied default distributions for the iTraxx-CJ tranches by means of the Principle of Maximum Entropy. The profiles are quite different from those of some popular probabilistic models. We show how to analyze the correlation structures, the conditional default probabilities p_i,j and conditional default correlations ρ_i,j. Here the subscript _i,j means that the default probability and correlation are estimated under i obligors are defaulted and j obligors are non-defaulted among N obligors. The implied default distribution, ρ_i,0 shows singular behavior, jumps high and then decreases rapidly to zero with i. Correspondingly p_i,0 increases with i and saturates to some maximum value below 1. Such a behavior implies that the credit market expects a middle-size avalanche. We also discuss the "True" default correlation implied by the market quotes.

Keywords: Implied default distribution, Entropy, correlation, iTraxx-CJ.

PACS: 89.65.-s, 02.50.-r.

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