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Pricing CDOs with state-dependent stochastic recovery rates

Author

Listed:
  • Salah Amraoui
  • Laurent Cousot
  • Sebastien Hitier
  • Jean-Paul Laurent

Abstract

Up to the 2007 crisis, research within bottom-up CDO models mainly concentrated on the dependence between defaults. Since then, due to substantial increases in market prices of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we use stochastic orders theory to assess the impact of recovery on CDOs and show that, in a factor copula framework, a decrease of recovery rates leads to an increase of the expected loss on senior tranches, even though the expected loss on the portfolio is kept fixed. This result applies to a wide range of latent factor models and is not specific to the Gaussian copula model. We then suggest introducing stochastic recovery rates in such a way that the conditional on the factor expected loss (or, equivalently, the large portfolio approximation) is the same as in the recovery markdown case. However, granular portfolios behave differently. We show that a markdown is associated with riskier portfolios than when using the stochastic recovery rate framework. As a consequence, the expected loss on a senior tranche is larger in the former case, whatever the attachment point. We also deal with implementation and numerical issues related to the pricing of CDOs within the stochastic recovery rate framework. Due to differences across names regarding the conditional (on the factor) losses given default, the standard recursion approach becomes problematic. We suggest approximating the conditional on the factor loss distributions, through expansions around some base distribution. Finally, we show that the independence and comonotonic cases provide some easy to compute bounds on expected losses of senior or equity tranches.

Suggested Citation

  • Salah Amraoui & Laurent Cousot & Sebastien Hitier & Jean-Paul Laurent, 2012. "Pricing CDOs with state-dependent stochastic recovery rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(8), pages 1219-1240, February.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:8:p:1219-1240
    DOI: 10.1080/14697688.2012.663925
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    References listed on IDEAS

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    1. Sudheer Chava & Catalina Stefanescu & Stuart Turnbull, 2011. "Modeling the Loss Distribution," Management Science, INFORMS, vol. 57(7), pages 1267-1287, July.
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    Cited by:

    1. Beer, Simone & Braun, Alexander & Marugg, Andrin, 2019. "Pricing industry loss warranties in a Lévy–Frailty framework," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 171-181.
    2. Meng-Jou Lu & Cathy Yi-Hsuan Chen & Wolfgang Karl Härdle, 2017. "Copula-based factor model for credit risk analysis," Review of Quantitative Finance and Accounting, Springer, vol. 49(4), pages 949-971, November.
    3. Fermanian, Jean-David, 2014. "The limits of granularity adjustments," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 9-25.
    4. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers 2013-27, Center for Research in Economics and Statistics.
    5. Albert Cohen & Nick Costanzino, 2017. "Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model," Risks, MDPI, vol. 5(2), pages 1-28, April.
    6. Castellano, Rosella & Corallo, Vincenzo & Morelli, Giacomo, 2022. "Structural estimation of counterparty credit risk under recovery risk," Journal of Banking & Finance, Elsevier, vol. 140(C).
    7. Lu, Meng-Jou & Chen, Cathy Yi-Hsuan & Härdle, Karl Wolfgang & Härdle, 2015. "Copula-Based Factor Model for Credit Risk Analysis," SFB 649 Discussion Papers SFB649DP2015-042, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Meng-Jou Lu & Cathy Yi-Hsuan Chen & Wolfgang Karl Hardle, 2020. "Copula-Based Factor Model for Credit Risk Analysis," Papers 2009.12092, arXiv.org, revised Oct 2020.

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