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Pricing Interest Rate-SensitiveCredit Portfolio Derivatives

Author

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  • Philippe Ehlers

    (ETH Zurich, D-Math)

  • Philipp J. Schonbucher

    (ETH Zurich, D-Math)

Abstract

In this paper we present a modelling framework for portfolio credit risk which incorporates the dependence between risk-free interest-rates and the default loss process. The contribution in this approach is that { besides the traditional diffusion based covariation between loss intensities and interest-rates { a direct dependence between interest-rates and the loss process is allowed, in particular default-free interest-rates can also depend on the loss history of the credit portfolio. Amongst other things this enables us to capture the effect that economy-wide default events are likely to have on government bond markets and/or central banks' interest-rate policies. Similar to Schonbucher (2005), the model is set up using a set of losscontingent forward interest-rates fn(t; T) and loss-contingent forward credit protection rates Fn(t; T) to parameterize the market prices of default-free bonds and credit-sensitive assets such as CDOs. We show that (up to weak regularity conditions), existence of such a parametrization is necessary and sufficient for the absence of static arbitrage opportunities in the underlying assets. We also give necessary conditions and sucient conditions on the dynamics of the parametrization which ensure absence of dynamic arbitrage opportunities in the model. Similar to the HJM drift restrictions for default-free interest-rates, these conditions take the form of restrictions on the drifts of fn(t; T) and Fn(t; T), together with a set of regularity conditions.

Suggested Citation

  • Philippe Ehlers & Philipp J. Schonbucher, 2006. "Pricing Interest Rate-SensitiveCredit Portfolio Derivatives," Swiss Finance Institute Research Paper Series 06-39, Swiss Finance Institute, revised Dec 2006.
  • Handle: RePEc:chf:rpseri:rp39
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    File URL: http://ssrn.com/abstract=957744
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    Cited by:

    1. Tao Peng, 2010. "Portfolio Credit Risk Modelling and CDO Pricing - Analytics and Implied Trees from CDO Tranches," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 8, january-d.

    More about this item

    Keywords

    AP; MI; Credit Portfolio Risk; Top-Down; Forward Model; Contagion; Collateralized Debt Obligations;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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