IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0812.4156.html
   My bibliography  Save this paper

Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisis

Author

Listed:
  • Massimo Morini
  • Damiano Brigo

Abstract

In this work we consider three problems of the standard market approach to pricing of credit index options: the definition of the index spread is not valid in general, the usually considered payoff leads to a pricing which is not always defined, and the candidate numeraire one would use to define a pricing measure is not strictly positive, which would lead to a non-equivalent pricing measure. We give a general mathematical solution to the three problems, based on a novel way of modeling the flow of information through the definition of a new subfiltration. Using this subfiltration, we take into account consistently the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show that, while the related mispricing can be negligible for standard options in normal market conditions, it can become highly relevant for different options or in stressed market conditions. In particular, we show on 2007 market data that after the subprime credit crisis the mispricing of the market formula compared to the no arbitrage formula we propose has become financially relevant even for the liquid Crossover Index Options.

Suggested Citation

  • Massimo Morini & Damiano Brigo, 2008. "Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisis," Papers 0812.4156, arXiv.org.
    • Handle: RePEc:arx:papers:0812.4156
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0812.4156
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, August.
    3. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2007. "Large Deviations In Multifactor Portfolio Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 345-379, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jose Giancarlo Gasha & Mr. Andre O Santos & Mr. Jorge A Chan-Lau & Mr. Carlos I. Medeiros & Mr. Marcos R Souto & Christian Capuano, 2009. "Recent Advances in Credit Risk Modeling," IMF Working Papers 2009/162, International Monetary Fund.
    2. Rama Cont & Yu Hang Kan, 2011. "Dynamic hedging of portfolio credit derivatives," Post-Print hal-00578008, HAL.

    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. 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.
    2. 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.
    3. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    4. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    5. Roberto Baviera, 2017. "Back-of-the-envelope swaptions in a very parsimonious multicurve interest rate model," Papers 1712.06466, arXiv.org.
    6. Fisher, Travis & Pulido, Sergio & Ruf, Johannes, 2019. "Financial models with defaultable numéraires," LSE Research Online Documents on Economics 84973, London School of Economics and Political Science, LSE Library.
    7. Kokholm, Thomas, 2008. "Pricing of Traffic Light Options and other Correlation Derivatives," Finance Research Group Working Papers F-2008-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    8. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    9. Pierre-Edouard Arrouy & Alexandre Boumezoued & Bernard Lapeyre & Sophian Mehalla, 2022. "Economic Scenario Generators: a risk management tool for insurance," Working Papers hal-03671943, HAL.
    10. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    11. Ernst Eberlein & Nataliya Koval, 2006. "A cross-currency Levy market model," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 465-480.
    12. Maria Siopacha & Josef Teichmann, 2007. "Weak and Strong Taylor methods for numerical solutions of stochastic differential equations," Papers 0704.0745, arXiv.org.
    13. Reik Borger & Jan van Heys, 2010. "Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 453-469.
    14. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    15. Carol Alexander & Dimitri Lvov, 2003. "Statistical Properties of Forward Libor Rates," ICMA Centre Discussion Papers in Finance icma-dp2003-03, Henley Business School, University of Reading.
    16. Glasserman, P. & Zhao, X., 1998. "Arbitrage-Free Discretization of Lognormal Forward Libor and Swap Rate Models," Papers 98-09, Columbia - Graduate School of Business.
    17. Beveridge, Christopher & Joshi, Mark & Tang, Robert, 2013. "Practical policy iteration: Generic methods for obtaining rapid and tight bounds for Bermudan exotic derivatives using Monte Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1342-1361.
    18. Linlin Xu & Giray Ökten, 2015. "High-performance financial simulation using randomized quasi-Monte Carlo methods," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1425-1436, August.
    19. Roberto Baviera, 2019. "Back-Of-The-Envelope Swaptions In A Very Parsimonious Multi-Curve Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-24, August.
    20. Tiziana Di Matteo & Tomaso Aste, 2002. "How Does The Eurodollar Interest Rate Behave?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 107-122.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:0812.4156. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.