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Copula-Based Model for the Term Structure of CDO Tranches

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The document discusses using copula functions to model the cross-sectional and temporal dependence of losses for CDO tranches. It proposes representing the dependence between increments of losses over time periods and cumulative losses at the start of periods through copula functions. This allows constructing a recursive algorithm to compute the propagation of losses over time and derive a term structure of tranche premiums consistent with the cross-sectional and temporal dependence structure. The approach must be modified for credit losses due to losses being bounded, including constraints in the algorithm.

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A Copula-Based Model of the Term Structure of CDO Tranches U. Cherubini – S. Mulinacci – S. Romagnoli University of Bologna International Financial Research Forum Paris, 27-28 March 2008
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object]
Copula applications in finance ,[object Object],[object Object],[object Object]
Dependence in finance ,[object Object],[object Object],[object Object],[object Object]
Equity: Barrier Altiplano ,[object Object],[object Object],[object Object],[object Object],[object Object]
Basket credit derivatives and CDOs ,[object Object],[object Object]
Tranches as options on losses ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Credit: Standard synthetic CDOs ,[object Object],[object Object],[object Object]
Cross-section dependence ,[object Object],[object Object],[object Object]
Temporal dependence ,[object Object],[object Object],[object Object]
Copula applications: literature ,[object Object],[object Object],[object Object],[object Object],[object Object]
Copula product ,[object Object],[object Object],[object Object]
Markov processes and copulas ,[object Object],[object Object],[object Object]
Properties of  products ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example: Brownian Copula ,[object Object],[object Object]
Time Changed Brownian Copulas ,[object Object],[object Object],[object Object]
Our approach: dependent increments ,[object Object],[object Object],[object Object]
A special class of processes ,[object Object],[object Object],[object Object],[object Object],[object Object]
A temporal aggregation algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Time aggregation with Archimedean copulas: tau = 0.2
Application to credit ,[object Object],[object Object],[object Object],[object Object]
Default probability of equity tranches: LPM, different time horizons
“ Houston, we have a problem” ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusions ,[object Object],[object Object],[object Object]

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Copula-Based Model for the Term Structure of CDO Tranches

  • 1. A Copula-Based Model of the Term Structure of CDO Tranches U. Cherubini – S. Mulinacci – S. Romagnoli University of Bologna International Financial Research Forum Paris, 27-28 March 2008
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  • 20. Time aggregation with Archimedean copulas: tau = 0.2
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  • 22. Default probability of equity tranches: LPM, different time horizons
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