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CMS Rate Convexity Adjustment A method is presented to calculating a particular multiplicative factor, which appears in a formula for a CMS rate convexity adjustment. A CMS rate convexity adjustment provides a correction term to the forward CMS rate to match the mean value of the CMS rate under the forward probability measure. We model the probability density of a CMS rate, under the forward swap measure, by a certain weighted sum of three log-normal densities. The defining parameter values for the log-normal densities above are determined by matching, in a least squares sense, the market price for various European style swaptions. The model returns the ratio of the variance of the CMS rate, under the distributional assumptions above, to the variance of the CMS rate, instead assuming that it is log-normally distributed under the forward swap measure. Some are unknown parameter values. The parameter values (1a-c) are determined by matching the model price for various European style swaptions, specified by respective Additionally, we determine the volatility parameter, , by matching the price of an at-the-money European style payer swaption.
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