Constant Maturity Credit Default Swap Pricing with Market Models

TL;DR

This paper develops an approximate market valuation formula for Constant Maturity Credit Default Swaps (CMCDS), incorporating a convexity adjustment, based on market models and forward CDS rate dynamics.

Contribution

It introduces a novel approximation formula for CMCDS pricing that extends existing market models to include a convexity adjustment term.

Findings

The formula reduces to a deterministic spread in zero-correlation cases.

Numerical examples illustrate the impact of the convexity adjustment.

The approach generalizes the LIBOR market model to credit derivatives.

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.