IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v09y2006i03ns0219024906003597.html
   My bibliography  Save this article

The Stochastic Intensity Ssrd Model Implied Volatility Patterns For Credit Default Swap Options And The Impact Of Correlation

Author

Listed:
  • DAMIANO BRIGO

    (Credit Models, Banca IMI, Corso Matteotti 6, 20121 Milano, Italy)

  • LAURENT COUSOT

    (Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA)

Abstract

In this paper we investigate implied volatility patterns in the Shifted Square Root Diffusion (SSRD) model as functions of the model parameters. We begin by recalling the Credit Default Swap (CDS) options market model that is consistent with a market Black-like formula, thus introducing a notion of implied volatility for CDS options. We examine implied volatilities coming from SSRD prices and characterize the qualitative behavior of implied volatilities as functions of the SSRD model parameters. We introduce an analytical approximation for the SSRD implied volatility that follows the same patterns in the model parameters and that can be used to have a first rough estimate of the implied volatility following a calibration. We compute numerically the CDS-rate volatility smile for the adopted SSRD model. We find a decreasing pattern of SSRD implied volatilities in the interest-rate/intensity correlation. We check whether it is possible to assume zero correlation after the option maturity in computing the option price.

Suggested Citation

  • Damiano Brigo & Laurent Cousot, 2006. "The Stochastic Intensity Ssrd Model Implied Volatility Patterns For Credit Default Swap Options And The Impact Of Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 315-339.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:03:n:s0219024906003597
    DOI: 10.1142/S0219024906003597
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024906003597
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024906003597?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Schönbucher, Philipp J., 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers 15/2001, University of Bonn, Bonn Graduate School of Economics (BGSE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bao, Qunfang & Li, Shenghong & Liu, Guimei, 2010. "Survival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing," MPRA Paper 27698, University Library of Munich, Germany, revised 27 Dec 2010.
    2. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    3. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2007.
    4. Jakob Sidenius & Vladimir Piterbarg & Leif Andersen, 2008. "A New Framework For Dynamic Credit Portfolio Loss Modelling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 163-197.
    5. Fabio Mercurio, 2010. "Modern Libor Market Models: Using Different Curves For Projecting Rates And For Discounting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 113-137.
    6. Joao B. C. Garcia & Helmut van Ginderen & Reinaldo C. Garcia, 2003. "On the Pricing of Credit Spread Options: A Two Factor HW–BK Algorithm," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 491-505.
    7. Gaspar, Raquel M. & Schmidt, Thorsten, 2005. "Quadratic Portfolio Credit Risk models with Shot-noise Effects," SSE/EFI Working Paper Series in Economics and Finance 616, Stockholm School of Economics.
    8. Houweling, Patrick & Vorst, Ton, 2005. "Pricing default swaps: Empirical evidence," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1200-1225, December.
    9. Bao, Qunfang & Chen, Si & Liu, Guimei & Li, Shenghong, 2010. "Unilateral CVA for CDS in Contagion model: With volatilities and correlation of spread and interest," MPRA Paper 28250, University Library of Munich, Germany, revised 27 Dec 2010.
    10. Roberto Casarin, 2005. "Stochastic Processes in Credit Risk Modelling," Working Papers ubs0505, University of Brescia, Department of Economics.
    11. Njike Leunga, Charles Guy & Hainaut, Donatien, 2019. "Interbank Credit Risk Modelling with Self-Exciting Jump Processes," LIDAM Discussion Papers ISBA 2019017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(3), pages 257-275, August.
    13. Hatem Ben-Ameur & Damiano Brigo & Eymen Errais, 2009. "A dynamic programming approach for pricing CDS and CDS options," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 717-726.
    14. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 31, July-Dece.
    15. Zorana Grbac & Antonis Papapantoleon, 2012. "A tractable LIBOR model with default risk," Papers 1202.0587, arXiv.org, revised Oct 2012.
    16. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
    17. Calice, Giovanni, 2011. "The Impact of Collateral Policies on Sovereign CDS Spreads," ECMI Papers 12234, Centre for European Policy Studies.
    18. Damien Ackerer & Damir Filipović, 2020. "Linear credit risk models," Finance and Stochastics, Springer, vol. 24(1), pages 169-214, January.
    19. Bao, Qunfang & Chen, Si & Liu, Guimei & Li, Shenghong, 2010. "Unilateral CVA for CDS in Contagion Model_with Volatilities and Correlation of Spread and Interest," MPRA Paper 26277, University Library of Munich, Germany.
    20. Ms. Elena Loukoianova & Salih N. Neftci & Mr. Sunil Sharma, 2006. "Pricing and Hedging of Contingent Credit Lines," IMF Working Papers 2006/013, International Monetary Fund.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:09:y:2006:i:03:n:s0219024906003597. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.