A Dynamic Programming Approach for Pricing CDS and CDS Options

Abstract

We propose a general setting for pricing single-name knock-out options. 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 calibration-based method and a historical 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 and not credit default.

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

JEL Classification: G12, G13