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Correlation Structures of Correlated Binomial Models and Implied Default Distribution

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

September 18, 2008

Abstract: We show how to analyze and interpret the correlation structures, the conditional expectation values and correlation coefficients of exchangeable Bernoulli random variables. We study implied default distributions for the iTraxx-CJ tranches and some popular probabilistic models, including the Gaussian copula model, Beta binomial distribution model and long-range Ising model. We interpret the differences in their profiles in terms of the correlation structures. The implied default distribution has singular correlation structures, reflecting the credit market implications. We point out two possible origins of the singular behavior.

Keywords: correlation, calibration, Beta binomial, Gaussian copula model, default, dependency structure, Ising model.

Published in: Journal of the Physical Society of Japan, Vol. 77, No. 11, (November 2008), pp. 114802-114808.

Previously titled: Default Distribution and Credit Market Implications

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