Pricing Credit Derivatives with Rating Transitions

Abstract

We develop a model for pricing risky debt and valuing credit derivatives that is easily calibrated to existing variables. Our approach is based on expanding the Heath-Jarrow-Morton (1990) term-structure model and its extension, the Das-Sundaram (2000) model to allow for defaultable debt with rating transitions. The framework has two salient features, comprising extensions over the earlier work: (i) it employs a rating transition matrix as the driver for the default process, and (ii) the entire set of rating categories is calibrated jointly, allowing, with minimal assumptions, arbitrage-free restrictions across rating classes, as a bond migrates amongst them. We provide an illustration of the approach by applying it to price credit sensitive notes that have coupon payments that are linked to the rating of the underlying credit.

Keywords: Risky debt, rating transitions, credit derivatives, credit sensitive note, HJM model

JEL Classification: G12, G13