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.