A dynamic programming approach for pricing CDS and CDS options

Abstract

We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled 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.Credit derivatives, Credit default swaps, Bermudan options, Dynamic programming, Doubly stochastic Poisson process, Cox process,

A CDS Option Miscellany

“…We could simply start with a hazard rate model formulation, and build everything up from first principles. This is the approach taken by more recent authors such as [1,3]. However, we would lose equivalence with Black76 in the all-running case, even for a lognormal hazard rate model.…”

“…The valuation of single-name options with running spread was originally performed in the Black'76 framework some years ago [8,12,13]. In this article we briefly review it and develop the subject to point out what happens when the strike is part-upfront, by which we mean that on exercise the CDS protection is to be paid wholly or partly upfront rather than all-runningwhich is how contracts now trade 1 . Upfronts introduce complications.…”

An Exact Formula for Default Swaptions’ Pricing in the SSRJD Stochastic Intensity Model

“…Given its relative tractability, the model can thus be calibrated to vanilla default swaptions in order to price more exotic products. A first attempt at Bermudan default options pricing for example is in Ben Ameur, Brigo, and Errais (2010), where the basic SSRD model is used. The jump‐extended SSRJD introduced here could be used as an improved version.…”