A Dynamic Programming Approach for Pricing CDS and CDS Options

by Hatem Ben-Ameur of HEC Montréal,
Damiano Brigo of Banca IMI, and
Eymen Errais of Stanford University

March 18, 2006

Abstract: We propose a general setting for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDS), European and Bermudan CDS options. The default of the underlying reference entity is modeled within a doubly stochastic framework where the default intensity follows a CIR++ process. We estimate the model parameters through a combination of a cross sectional calibration-based method and a historical estimation approach. We propose a numerical procedure based on dynamic programming and a piecewise linear approximation to price American-style knock-out credit options. Our numerical investigation shows consistency, convergence and efficiency. We find that American-style CDS options can complete the credit derivatives market by allowing the investor to focus on spread movements rather than on the default event.

JEL Classification:   G12, G13.

Keywords: Credit Derivatives, Credit Default Swaps, Bermudan Options, Dynamic Programming, Doubly Stochastic Poisson, Cox Process.

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