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 Das and Sundaram (2000) extension of the Heath-Jarrow-Morton (1990) term-structure model to allow for multiple ratings classes of debt. The framework has two salient features: (i) it employs a ratings transition matrix as the driver or the default process, and (ii) the entire set of rating categories is calibrated jointly, allowing 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.