IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v116y2006i4p690-698.html
   My bibliography  Save this article

A reflection principle for correlated defaults

Author

Listed:
  • Patras, Frédéric

Abstract

The correct valuation of the so-called "correlation products" in the credit risk market such as n-th-to-default swaps or CDOs requires a better understanding of higher dimensional barrier default phenomena. We introduce a reflection principle suited for the pricing of credit derivatives on two securities, paving the way for the development of new methods in the field. For that purpose, we introduce new processes, the distributions of which involve generalized Bessel functions. As an application, we derive a closed formula for second-to-default digital swaps, under the standard Black-Cox hypothesis on the conditions triggering default.

Suggested Citation

  • Patras, Frédéric, 2006. "A reflection principle for correlated defaults," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 690-698, April.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:4:p:690-698
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00162-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    2. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
    3. Hua He & William P. Keirstead & Joachim Rebholz, 1998. "Double Lookbacks," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 201-228, July.
    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. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    2. Abínzano, Isabel & Seco, Luis & Escobar, Marcos & Olivares, Pablo, 2009. "Single and Double Black-Cox: Two approaches for modelling debt restructuring," Economic Modelling, Elsevier, vol. 26(5), pages 910-917, September.
    3. Mercadier, Mathieu & Lardy, Jean-Pierre, 2019. "Credit spread approximation and improvement using random forest regression," European Journal of Operational Research, Elsevier, vol. 277(1), pages 351-365.
    4. Nystrom, Kaj & Skoglund, Jimmy, 2006. "A credit risk model for large dimensional portfolios with application to economic capital," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2163-2197, August.
    5. International Association of Deposit Insurers, 2011. "Evaluation of Deposit Insurance Fund Sufficiency on the Basis of Risk Analysis," IADI Research Papers 11-11, International Association of Deposit Insurers.
    6. Ulrich Erlenmaier & Hans Gersbach, 2014. "Default Correlations in the Merton Model," Review of Finance, European Finance Association, vol. 18(5), pages 1775-1809.
    7. Mark B. Wise & Vineer Bhansali, 2002. "Portfolio Allocation to Corporate Bonds with Correlated Defaults," Papers nlin/0205011, arXiv.org, revised Jun 2002.
    8. 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, July-Dece.
    9. Chamizo, Álvaro & Fonollosa, Alexandre & Novales, Alfonso, 2019. "Forward-looking asset correlations in the estimation of economic capital," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 61(C), pages 264-288.
    10. Alexander Lipton & Andrey Gal & Andris Lasis, 2014. "Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1899-1922, November.
    11. Marcos Escobar & Peter Hieber & Matthias Scherer, 2014. "Efficiently pricing double barrier derivatives in stochastic volatility models," Review of Derivatives Research, Springer, vol. 17(2), pages 191-216, July.
    12. Weiping Li & Tim Krehbiel, 2016. "An Improved Approach To Evaluate Default Probabilities And Default Correlations With Consistency," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-29, August.
    13. Alfred Hamerle & Daniel Rösch, 2003. "Risikofaktoren und Korrelationen für Bonitätsveränderungen," Schmalenbach Journal of Business Research, Springer, vol. 55(3), pages 199-223, May.
    14. Albrecht, Peter, 2005. "Kreditrisiken - Modellierung und Management: Ein Überblick," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 1(2), pages 22-152.
    15. Hamerle, Alfred & Liebig, Thilo & Rösch, Daniel, 2003. "Credit Risk Factor Modeling and the Basel II IRB Approach," Discussion Paper Series 2: Banking and Financial Studies 2003,02, Deutsche Bundesbank.
    16. Sheen Liu & Howard Qi & Jian Shi & Yan Alice Xie, 2015. "Inferring Default Correlation from Equity Return Correlation," European Financial Management, European Financial Management Association, vol. 21(2), pages 333-359, March.
    17. Hamerle, Alfred & Liebig, Thilo & Scheule, Harald, 2004. "Forecasting Credit Portfolio Risk," Discussion Paper Series 2: Banking and Financial Studies 2004,01, Deutsche Bundesbank.
    18. Mark B. Wise & Vineer Bhansali, 2002. "Implications of Correlated Default For Portfolio Allocation To Corporate Bonds," Papers nlin/0209010, arXiv.org.
    19. Alexander Lipton & Ioana Savescu, 2012. "A structural approach to pricing credit default swaps with credit and debt value adjustments," Papers 1206.3104, arXiv.org.
    20. Peter Christoffersen & Kris Jacobs & Xisong Jin & Hugues Langlois, 2013. "Dynamic Diversification in Corporate Credit," CREATES Research Papers 2013-46, Department of Economics and Business Economics, Aarhus University.

    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:eee:spapps:v:116:y:2006:i:4:p:690-698. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.