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

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 et al., 2006) on the static loss-surface model to a model containing the necessary underlying dynamics. JEL classification code: G13 keywords: forward-start CDO’s, FCDO’s, options on CDO’s, calibration 1Department of Physics, University of Toronto, Toronto, ON M5S 1A7, CANADA; email: [email protected]; telephone: (416) 978-3821. 2I thank Julien Houdain and Fortis Investments for providing the market quotes used in the examples, and acknowledge the collaboration of Alexandru Badescu in obtaining the results of the appendix. I also thank Jon Gregory for useful discussions of leveraged super-senior tranches. The support of the Natural Sciences and Engineering Research Council of Canada