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An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model


  • Damiano Brigo
  • Naoufel El-Bachir


We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consistently. We show with numerical experiments that the model implies plausible volatility smiles.

Suggested Citation

  • Damiano Brigo & Naoufel El-Bachir, 2008. "An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model," Papers 0812.4199,
  • Handle: RePEc:arx:papers:0812.4199

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    References listed on IDEAS

    1. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    2. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, August.
    3. Damiano Brigo & Naoufel El-Bachir, 2006. "Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model," ICMA Centre Discussion Papers in Finance icma-dp2006-13, Henley Business School, Reading University.
    4. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    5. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    6. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    7. 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. Michele Leonardo Bianchi, 2012. "An empirical comparison of alternative credit default swap pricing models," Temi di discussione (Economic working papers) 882, Bank of Italy, Economic Research and International Relations Area.
    2. Tomasz Bielecki & Monique Jeanblanc & Marek Rutkowski, 2011. "Hedging of a credit default swaption in the CIR default intensity model," Finance and Stochastics, Springer, vol. 15(3), pages 541-572, September.
    3. Damiano Brigo & Kyriakos Chourdakis & Imane Bakkar, 2009. "Counterparty risk valuation for Energy-Commodities swaps: Impact of volatilities and correlation," Papers 0901.1099,
    4. Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2009. "Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations," Papers 0911.3331,, revised Feb 2010.
    5. Damiano Brigo, 2011. "Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending," Papers 1111.1331,, revised Jun 2012.
    6. Richard J Martin, 2011. "A CDS Option Miscellany," Papers 1201.0111,, revised Sep 2017.
    7. Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2009. "Credit models and the crisis, or: how I learned to stop worrying and love the CDOs," Papers 0912.5427,, revised Feb 2010.
    8. Damiano Brigo & Massimo Morini & Marco Tarenghi, 2009. "Credit Calibration with Structural Models: The Lehman case and Equity Swaps under Counterparty Risk," Papers 0912.4404,
    9. Damiano Brigo & Mirela Predescu & Agostino Capponi, 2010. "Credit Default Swaps Liquidity modeling: A survey," Papers 1003.0889,, revised Mar 2010.
    10. Amelie Hüttner & Matthias Scherer, 2016. "A note on the valuation of CDS options and extension risk in a structural model with jumps," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 1-16, June.
    11. Naoufel El-Bachir & Damiano Brigo, 2008. "An analytically tractable time-changed jump-diffusion default intensity model," ICMA Centre Discussion Papers in Finance icma-dp2008-06, Henley Business School, Reading University.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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