Simultaneous Calibration to a Range of Portfolio Credit Derivatives with a Discrete-Time Multi-Step Markov Loss Model

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Simultaneous Calibration to a Range of Portfolio Credit Derivatives with a Discrete-Time Multi-Step Markov Loss Model

by Michael B. Walker of the University of Toronto

August 29, 2007

Abstract: This article describes a dynamic discrete-time multi-step Markov model for the losses experienced by a given credit portfolio, and develops a method for the simultaneous calibration of the model to all available relevant market prices (for CDO's, forward-start CDO's, options on CDO's, leveraged super-senior tranches with loss triggers, etc.) established on a given day. The implementation is via an efficient linear programming procedure, and examples are given. The approach represents an extension of previous work (Walker, 2005, 2006; Torresetti, Brigo and Pallavicini,2006) on the static loss-surface model to a model containing the necessary underlying dynamics.

JEL Classification: G13.

Keywords: calibration, multi-step Markov model, forward-start CDO's, options on CDO's, leveraged super-senior tranches.

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