Credit models and the crisis, or: how I learned to stop worrying and love the CDOs
We follow a long path for Credit Derivatives and Collateralized Debt Obligations (CDOs) in particular, from the introduction of the Gaussian copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time. En passant, we also illustrate the implied copula, a method that can consistently account for CDOs with different attachment and detachment points but not for different maturities. The discussion is abundantly supported by market examples through history. The dangers and critics we present to the use of the Gaussian copula and of implied correlation had all been published by us, among others, in 2006, showing that the quantitative community was aware of the model limitations before the crisis. We also explain why the Gaussian copula model is still used in its base correlation formulation, although under some possible extensions such as random recovery. Overall we conclude that the modeling effort in this area of the derivatives market is unfinished, partly for the lack of an operationally attractive single-name consistent dynamic loss model, and partly because of the diminished investment in this research area.
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- Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2009. "Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations," Papers 0911.3331, arXiv.org, revised Feb 2010.
- Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
- Torresetti, Roberto & Pallavicini, Andrea, 2007. "Stressing rating criteria allowing for default clustering: the CPDO case," MPRA Paper 17104, University Library of Munich, Germany, revised 04 Sep 2009.
- Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2007. "Cluster-Based Extension Of The Generalized Poisson Loss Dynamics And Consistency With Single Names," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 607-631.
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- Francis A. Longstaff & Arvind Rajan, 2006.
"An Empirical Analysis of the Pricing of Collateralized Debt Obligations,"
NBER Working Papers
12210, National Bureau of Economic Research, Inc.
- Francis A. Longstaff & Arvind Rajan, 2008. "An Empirical Analysis of the Pricing of Collateralized Debt Obligations," Journal of Finance, American Finance Association, vol. 63(2), pages 529-563, 04.
- Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
- Damiano Brigo & Naoufel El-Bachir, 2007.
"An exact formula for default swaptions’ pricing in the SSRJD stochastic intensity model,"
ICMA Centre Discussion Papers in Finance
icma-dp2007-14, Henley Business School, Reading University.
- Damiano Brigo & Naoufel El-Bachir, 2008. "An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model," Papers 0812.4199, arXiv.org.
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