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Credit models and the crisis, or: how I learned to stop worrying and love the CDOs

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  • Damiano Brigo
  • Andrea Pallavicini
  • Roberto Torresetti

Abstract

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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File URL: http://arxiv.org/pdf/0912.5427
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Paper provided by arXiv.org in its series Papers with number 0912.5427.

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Date of creation: Dec 2009
Date of revision: Feb 2010
Handle: RePEc:arx:papers:0912.5427

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  1. 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.
  2. Damiano Brigo & Naoufel El-Bachir, 2008. "An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model," Papers 0812.4199, arXiv.org.
  3. 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.
  4. Rosen, Dan & Saunders, David, 2009. "Analytical methods for hedging systematic credit risk with linear factor portfolios," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(1), pages 37-52, January.
  5. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 51(4), pages 621-51, October.
  6. 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., World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 607-631.
  7. 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., World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
  8. 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.
  9. Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, Springer, vol. 9(1), pages 29-42, January.
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Cited by:
  1. Vanini, Paolo, 2012. "Fiancial Innovation, Structuring and Risk Transfer," MPRA Paper 42536, University Library of Munich, Germany.
  2. Balakrishna, B S, 2010. "Levy Subordinator Model: A Two Parameter Model of Default Dependency," MPRA Paper 26274, University Library of Munich, Germany.
  3. Tim J. Brereton & Dirk P. Kroese & Joshua C. Chan, 2012. "Monte Carlo Methods for Portfolio Credit Risk," ANU Working Papers in Economics and Econometrics, Australian National University, College of Business and Economics, School of Economics 2012-579, Australian National University, College of Business and Economics, School of Economics.
  4. Balakrishna, B S, 2010. "Levy Subordinator Model of Default Dependency," MPRA Paper 21386, University Library of Munich, Germany.

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