CMS Convexity Adjustment

Characteristically, constant maturity swaps have unnatural time lags because a counterparty pays/receives the swap rate only in one payment, rather than paying/receiving it in a series of payments (annuity). The difference between the expected CMS rate and the implied forward swap rate under a swap measure is known as the CMS convexity adjustment. The adjustment is required due to the use of a different measure: implied forward rates are the expectations of the CMS rate under the given swap measure while constant maturity swaps require calculation of the CMS rates under a zero-coupon bond measure. Using a different measure, calculation of the CMS resets can start off with figuring out the forward swap rate, and then accounting for the CMS convexity adjustment.