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On break-even correlation: the way to price structured credit derivatives by replication

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Listed:
  • Jean-David Fermanian

    (CREST-ENSAE)

  • Olivier Vigneron

    (JP-Morgan)

Abstract

We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient conditions so that the corresponding asset prices are martingales and introduce the concept of "break-even" correlation matrix. When no sudden jump-to-default events occur, we show that the perfect replication of these payoffs under the GCM is obtained if and only if the underlying single name credit spreads follow a particular family of dynamics. We calculate the corresponding break-even correlations and we exhibit a class of Merton-style models that are consistent with this result. We explain why the GCM does not have a lot of competitors among the class of one-period static models, except perhaps the Clayton copula.

Suggested Citation

  • Jean-David Fermanian & Olivier Vigneron, 2012. "On break-even correlation: the way to price structured credit derivatives by replication," Papers 1204.2251, arXiv.org.
  • Handle: RePEc:arx:papers:1204.2251
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    File URL: http://arxiv.org/pdf/1204.2251
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    References listed on IDEAS

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    1. 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.
    2. Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
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