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Evaluation of tranche in securitization and long-range Ising model

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  • Kitsukawa, K.
  • Mori, S.
  • Hisakado, M.

Abstract

This econophysics work studies the long-range Ising model of a finite system with N spins and the exchange interaction J/N and the external field H as a model for homogeneous credit portfolio of assets with default probability Pd and default correlation ρd. Based on the discussion on the (J,H) phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for Pd,ρd and the normalization factor Z in terms of the model parameters N and J,H. The effect of the default correlation ρd on the probabilities P(Nd,ρd) for Nd defaults and on the cumulative distribution function D(i,ρd) are discussed. The latter means the average loss rate of the“tranche” (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with ρd and that of the senior tranche increases linearly, which are important in their pricing and ratings.

Suggested Citation

  • Kitsukawa, K. & Mori, S. & Hisakado, M., 2006. "Evaluation of tranche in securitization and long-range Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 191-206.
    • Handle: RePEc:eee:phsmap:v:368:y:2006:i:1:p:191-206
    DOI: 10.1016/j.physa.2005.12.057
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    References listed on IDEAS

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    1. Jordi Molins & Eduard Vives, 2004. "Long range Ising model for credit risk modeling in homogeneous portfolios," Papers cond-mat/0401378, arXiv.org.
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    Cited by:

    1. I. Onur Filiz & Xin Guo & Jason Morton & Bernd Sturmfels, 2008. "Graphical models for correlated defaults," Papers 0809.1393, arXiv.org.
    2. Kato, Kensuke, 2016. "Long-range Ising model for credit portfolios with heterogeneous credit exposures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1103-1119.
    3. Wu, Binghui, 2018. "Asset securitization and rate of return: A study on letters of guarantee," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1551-1554.
    4. J. Molins & E. Vives, 2015. "Model risk on credit risk," Papers 1502.06984, arXiv.org, revised Dec 2015.

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    3. K. Kitsukawa & S. Mori & M. Hisakado, 2006. "Evaluation of Tranche in Securitization and Long-range Ising Model," Papers physics/0603040, arXiv.org, revised Sep 2006.

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