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Pricing of CDOs based on the multivariate Wang transform

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  • Kijima, Masaaki
  • Motomiya, Shin-ichi
  • Suzuki, Yoichi

Abstract

This paper extends the one-factor Gaussian copula model, the standard market model for valuing CDOs, based on the multivariate Wang transform. Unlike the existing models, our model calibrates the parameter associated with a risk adjustment for default threshold, not correlation parameter, which always exists and is unique for any market price of CDO tranche. A Student t-copula model is also considered within the same framework to describe a fat-tail distribution observed in the actual market. Through numerical experiments, it is shown that our model provides a better fit to the market data compared with the existing models.

Suggested Citation

  • Kijima, Masaaki & Motomiya, Shin-ichi & Suzuki, Yoichi, 2010. "Pricing of CDOs based on the multivariate Wang transform," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2245-2258, November.
    • Handle: RePEc:eee:dyncon:v:34:y:2010:i:11:p:2245-2258
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    References listed on IDEAS

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    1. Jean-Paul Laurent & Jon Gregory, 2005. "Basket default swaps, CDOs and factor copulas," Post-Print hal-03679517, HAL.
    2. Kijima, Masaaki & Muromachi, Yukio, 2008. "An extension of the Wang transform derived from Bühlmann's economic premium principle for insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 887-896, June.
    3. Wang, Shaun S., 2002. "A Universal Framework for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 213-234, November.
    4. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    5. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    6. X. Burtschell & Jonathan Gregory & Jean-Paul Laurent, 2009. "A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework," Post-Print hal-03676448, HAL.
    7. Masaaki Kijima & Keiichi Tanaka & Tony Wong, 2009. "A multi-quality model of interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 133-145.
    8. Wang, Shaun S., 2003. "Equilibrium Pricing Transforms: New Results Using Buhlmann’s 1980 Economic Model," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 57-73, May.
    9. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Computational Statistics, Springer, vol. 18(3), pages 355-373, September.
    10. Kijima, Masaaki, 2006. "A Multivariate Extension of Equilibrium Pricing Transforms: The Multivariate Esscher and Wang Transforms for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 269-283, May.
    11. Masaaki Kijima & Masamitsu Ohnishi, 1996. "Portfolio Selection Problems Via The Bivariate Characterization Of Stochastic Dominance Relations1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 237-277, July.
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    1. Belzunce, Félix & Suárez-Llorens, Alfonso & Sordo, Miguel A., 2012. "Comparison of increasing directionally convex transformations of random vectors with a common copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 385-390.

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