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Constant Maturity Credit Default Swap Pricing with Market Models

by Damiano Brigo of Banca IMI

March 2, 2005

Abstract: In this work we derive an approximated no-arbitrage market valuation formula for Constant Maturity Credit Default Swaps (CMCDS). We move from the CDS options market model in Brigo (2004), and derive a formula for CMCDS that is the analogous of the formula for constant maturity swaps in the default free swap market under the LIBOR market model. A "convexity adjustment"-like correction is present in the related formula. Without such correction, or with zero correlations, the formula returns an obvious deterministic-credit-spread expression for the CMCDS price. To obtain the result we derive a joint dynamics of forward CDS rates under a single pricing measure, as in Brigo (2004). Numerical examples of the "convexity adjustment" impact complete the paper.

Keywords: CDS Options, CDS Options Market Model, Constant Maturity CDS, Convexity Adjustment, Participation Rate, CDS rates volatility, CDS rates correlation.

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