Calibration of CDO Tranches with the Dynamical Generalized-Poisson Loss Model

35 Pages Posted: 11 May 2006 Last revised: 30 Apr 2010

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Roberto Torresetti

Banco Popolare

Date Written: May 3, 2007

Abstract

In the first part we consider a dynamical model for the number of defaults of a pool of names. The model is based on the notion of generalized Poisson process, allowing for more than one default in small time intervals, contrary to many alternative approaches to loss modeling. We illustrate how to define the pool default intensity and discuss recovery assumptions. The models are tractable, pricing and simulation are straightforward, and consistent calibration to quoted index CDO tranches and tranchelets for several maturities is feasible, as we illustrate with numerical examples. In the second part we model directly the pool loss and we introduce extensions based on piecewise-gamma, scenario-based or CIR random intensities, leading to richer spread dynamics, investigating calibration improvements and stability.

Keywords: Loss Distribution, Loss Dynamics, Calibration, CDO Tranches and Tranchelets, Generalized Poisson Processes, Gamma intensity, Spread Dynamics

JEL Classification: G13

Suggested Citation

Brigo, Damiano and Pallavicini, Andrea and Torresetti, Roberto, Calibration of CDO Tranches with the Dynamical Generalized-Poisson Loss Model (May 3, 2007). Available at SSRN: https://ssrn.com/abstract=900549 or http://dx.doi.org/10.2139/ssrn.900549

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Andrea Pallavicini (Contact Author)

Banca IMI ( email )

Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

Roberto Torresetti

Banco Popolare ( email )

Milan
Italy

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