Constant Maturity Credit Default Swap Pricing with Market Models

Details Constant Maturity Credit Default Swap Pricing with Market Models Constant Maturity Credit Default Swap Pricing with Market Models

2008-12-22

arxiv.org/abs/0812.4159v1

Short version in Risk Magazine, june 2006 issue, and related paper in "Credit Risk: Models, Derivatives and Management", Taylo

Economy

Quantitative Finance

Pricing of Securities

Scientific paper

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.

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