Constant Maturity Credit Default Swap Pricing with Market Models

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

JEL Classification: G13