citi2 - Default Clustering and Pricing of CDO' s Xian Hua...

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Default Clustering and Pricing of CDO&s Xian Hua Peng and Steven Kou Columbia University 1 / 27
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1 The Recent Financial Turmoil 2 What is a CDO? 3 Current Portfolio Credit Risk Models 4 The New Conditional Survival (CS) Model 5 CDO Pricing under the CS Model 2 / 27
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The Recent Financial Turmoil The crisis in subprime credit markets Clustering defaults across time (time series correlation, Das et al. 2007) and cross-sectionally (contagion e/ect, Longsta/ and Rajan 2007) Di¢ culties in modeling collateralized debt obligations (CDOs) 3 ± 27
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What is a CDO What is a CDO (Collateralized Debt Obligation)? CDO is a security constructed from a portfolio of &xed-income securities or credit derivatives. CDO provides a way to create high quality debt out of a portfolio of low quality debt. 5 / 27
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CDO and Current Subprime Mortgage Crisis The impact of credit crunch on iTraxx 5Y index tranche spreads Tranches(%) 0-3 3-6 6-9 9-12 12-22 22-100 09/20/07 1812 84 37 23 15 7 03/14/08 5150 649 401 255 143 70 09/12/08 4011 475 277 152 68 35 CDO played an important role in the subprime mortgage crisis Rating Agencies Banks Mispricing and improper credit rating of CDO have been criticized. CDO itself should not be blamed for the &nancial crisis: it is a good instrument as long as one knows how to price it. 6 / 27
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The Market Standard & Gaussian Copula Models Idea: using copula functions to model default time correlation Literature: Gaussian copula model (Li, 2000) What is wrong with Gaussian copula? Gaussian copula cannot generate tail dependence lim q ! 1 P ( Y > VaR q ( Y ) j X > VaR q ( X )) = 0 Gaussian copula does not work during crisis, when the default correlation is strong. 8 / 27
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0-3% 3-6% 6-9% 9-12% 12-22% 22-100% 0 0.2 0.4 0.6 0.8 1 Tranche implied copula correlation Implied Copula Correlation of iTraxx 5Y CDO on 03/14/08 9 / 27
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Other Models Top-down approach builds models for the portfolio cumulative loss process directly Good &t for standard CDO portfolios, but with no connection to underlying single names Longsta/ and Rajan, 2007, Giesecke, et al., 2007, Halperin, 2007, Cont and Minca, 2007 Bottom-up approach builds models for single name default times Consistent with single name CDS spreads, but is hard to price and calibrate CDO tranches Examples: Static bottom-up models, e.g. copula models, dynamic intensity models 10 ± 27
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This note was uploaded on 10/18/2010 for the course IEOR 4702 taught by Professor Kou during the Spring '10 term at Columbia.

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citi2 - Default Clustering and Pricing of CDO' s Xian Hua...

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