IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2011.10101.html
   My bibliography  Save this paper

Affine Pricing and Hedging of Collateralized Debt Obligations

Author

Listed:
  • Zehra Eksi
  • Damir Filipovi'c

Abstract

This study deals with the pricing and hedging of single-tranche collateralized debt obligations (STCDOs). We specify an affine two-factor model in which a catastrophic risk component is incorporated. Apart from being analytically tractable, this model has the feature that it captures the dynamics of super-senior tranches, thanks to the catastrophic component. We estimate the factor model based on the iTraxx Europe data with six tranches and four different maturities, using a quasi-maximum likelihood (QML) approach in conjunction with the Kalman filter. We derive the model-based variance-minimizing strategy for the hedging of STCDOs with a dynamically rebalanced portfolio on the underlying swap index. We analyze the actual performance of the variance-minimizing hedge on the iTraxx Europe data. In order to assess the hedging performance further, we run a simulation analysis where normal and extreme loss scenarios are generated via the method of importance sampling. Both in-sample hedging and simulation analysis suggest that the variance-minimizing strategy is most effective for mezzanine tranches in terms of yielding less riskier hedging portfolios and it fails to provide adequate hedge performance regarding equity tranches.

Suggested Citation

  • Zehra Eksi & Damir Filipovi'c, 2020. "Affine Pricing and Hedging of Collateralized Debt Obligations," Papers 2011.10101, arXiv.org.
    • Handle: RePEc:arx:papers:2011.10101
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2011.10101
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    3. Alois L. J. Geyer & Stefan Pichler, 1999. "A State‐Space Approach To Estimate And Test Multifactor Cox‐Ingersoll‐Ross Models Of The Term Structure," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(1), pages 107-130, March.
    4. Long Chen & Pierre Collin-Dufresne & Robert S. Goldstein, 2009. "On the Relation Between the Credit Spread Puzzle and the Equity Premium Puzzle," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3367-3409, September.
    5. Rama Cont & Yu Hang Kan, 2011. "Dynamic hedging of portfolio credit derivatives," Post-Print hal-00578008, HAL.
    6. Gregory R. Duffee & Richard H. Stanton, 2012. "Estimation of Dynamic Term Structure Models," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-51.
    7. Frey, Rüdiger & Backhaus, Jochen, 2010. "Dynamic hedging of synthetic CDO tranches with spread risk and default contagion," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 710-724, April.
    8. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc, 2010. "Up and down credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1137-1151.
    9. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, January.
    10. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    11. Pierre Collin-Dufresne & Robert S. Goldstein & Fan Yang, 2012. "On the Relative Pricing of Long-Maturity Index Options and Collateralized Debt Obligations," Journal of Finance, American Finance Association, vol. 67(6), pages 1983-2014, December.
    12. Rama Cont & Andreea Minca, 2013. "Recovering portfolio default intensities implied by CDO quotes," Post-Print hal-00413730, HAL.
    13. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    14. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Ascheberg, Marius & Bick, Björn & Kraft, Holger, 2013. "Hedging structured credit products during the credit crisis: A horse race of 10 models," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1687-1705.
    16. Chen, Ren-Raw & Scott, Louis, 2003. "Multi-factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model," The Journal of Real Estate Finance and Economics, Springer, vol. 27(2), pages 143-172, September.
    17. Geyer, Alois L J & Pichler, Stefan, 1999. "A State-Space Approach to Estimate and Test Multifactor Cox-Ingersoll-Ross Models of the Term Structure," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(1), pages 107-130, Spring.
    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. Michele Leonardo Bianchi, 2018. "Are multi-factor Gaussian term structure models still useful? An empirical analysis on Italian BTPs," Papers 1805.09996, arXiv.org.
    2. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    3. Gonzalo Cortazar & Eduardo S. Schwartz & Lorenzo F. Naranjo, 2007. "Term-structure estimation in markets with infrequent trading," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(4), pages 353-369.
    4. Wolfgang Lemke & Deutsche Bundesbank, 2006. "Term Structure Modeling and Estimation in a State Space Framework," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-28344-7, October.
    5. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, December.
    6. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Management Science, INFORMS, vol. 60(9), pages 2248-2268, September.
    7. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2013. "Density approach in modelling multi-defaults," Working Papers hal-00870492, HAL.
    8. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    9. David Bolder, 2001. "Affine Term-Structure Models: Theory and Implementation," Staff Working Papers 01-15, Bank of Canada.
    10. Alejandro Bernales & Diether W. Beuermann & Gonzalo Cortazar, 2014. "Thinly traded securities and risk management," Estudios de Economia, University of Chile, Department of Economics, vol. 41(1 Year 20), pages 5-48, June.
    11. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2017. "Dynamics of multivariate default system in random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3943-3965.
    12. Cortazar, Gonzalo & Schwartz, Eduardo S. & Naranjo, Lorezo, 2003. "Term Structure Estimation in Low-Frequency Transaction Markets: A Kalman Filter Approach with Incomplete Panel-Data," University of California at Los Angeles, Anderson Graduate School of Management qt56h775cz, Anderson Graduate School of Management, UCLA.
    13. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi & Takami Tokioka, 2018. "On the Effect of Bank of Japan’s Outright Purchase on the JGB Yield Curve," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(1), pages 47-70, March.
    14. Choong Tze Chua & Dean Foster & Krishna Ramaswamy & Robert Stine, 2008. "A Dynamic Model for the Forward Curve," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 265-310, January.
    15. Yalin Gündüz & Marliese Uhrig-Homburg, 2014. "Does modeling framework matter? A comparative study of structural and reduced-form models," Review of Derivatives Research, Springer, vol. 17(1), pages 39-78, April.
    16. Jiyoung Lee, 2015. "Disentangling the Predictive Power of Term Spreads under Inflation Targeting," International Economic Journal, Taylor & Francis Journals, vol. 29(3), pages 419-450, September.
    17. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    18. Cortazar, Gonzalo & Beuermann, Diether & Bernales, Alejandro, 2013. "Risk Management with Thinly Traded Securities: Methodology and Implementation," IDB Publications (Working Papers) 4647, Inter-American Development Bank.
    19. De Rossi, Giuliano, 2004. "Kalman filtering of consistent forward rate curves: a tool to estimate and model dynamically the term structure," Journal of Empirical Finance, Elsevier, vol. 11(2), pages 277-308, March.

    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:2011.10101. 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.