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Evaluation of Tranche in Securitization and Long-range Ising Model

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

Abstract

This econophysics work studies the long-range Ising model of a finite system with $N$ spins and the exchange interaction $\frac{J}{N}$ and the external field $H$ as a modely for homogeneous credit portfolio of assets with default probability $P_{d}$ and default correlation $\rho_{d}$. Based on the discussion on the $(J,H)$ phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for $P_{d},\rho_{d}$ and the normalization factor $Z$ in terms of the model parameters $N$ and $J,H$. The effect of the default correlation $\rho_{d}$ on the probabilities $P(N_{d},\rho_{d})$ for $N_{d}$ defaults and on the cumulative distribution function $D(i,\rho_{d})$ 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 $\rho_{d}$ and that of the senior tranche increases linearly, which are important in their pricing and ratings.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:physics/0603040
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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. 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.
    3. 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.

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