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Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model

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  • Damiano Brigo

    ()

  • Naoufel El-Bachir

    ()
    (ICMA Centre, University of Reading)

Abstract

We present a two-factor stochastic default intensity and interest rate model for pricing single-name default swaptions. The specific positive square root processes considered fall in the relatively tractable class of affine jump diffusions while allowing for inclusion of stochastic volatility and jumps in default swap spreads. The parameters of the short rate dynamics are first calibrated to the interest rates markets, before calibrating separately the default intensity model to credit derivatives market data. A few variants of the model are calibrated in turn to market data, and different calibration procedures are compared. Numerical experiments show that the calibrated model can generate plausible volatility smiles. Hence, the model can be calibrated to a default swap term structure and few default swaptions, and the calibrated parameters can be used to value consistently other default swaptions (different strikes and maturities, or more complex structures) on the same credit reference name.

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File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2006-13.pdf
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Bibliographic Info

Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2006-13.

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Length: 22 pages
Date of creation: Dec 2006
Date of revision:
Handle: RePEc:rdg:icmadp:icma-dp2006-13

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Related research

Keywords: Credit derivatives; credit default; swap; credit default swaption; jump-diffusion; stochastic intensity; doubly stochastic poisson process; cox process;

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References

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  1. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, 08.
  2. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  3. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
  4. 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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Cited by:
  1. Damiano Brigo & Naoufel El-Bachir, 2008. "An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model," Papers 0812.4199, arXiv.org.

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