Pricing Credit Derivatives with Rating Transitions

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Abstract
We present a model for pricing risky debt and valuing credit derivatives that is easily calibrated to existing variables. Our approach expands a classical term-structure model to allow for multiple rating classes of debt. The framework has two salient features: (1) it uses a rating-transition matrix as the driver for the default process, and (2) the entire set of rating categories is calibrated jointly, which allows arbitrage-free restrictions across rating classes as a bond migrates among them. We illustrate the approach by applying it to price credit-sensitive notes that have coupon payments linked to the rating of the underlying credit.