Constant Maturity Swaps, Forward Measure and Libor Market Model

Constant maturity swaps can be regarded as generalizations of vanilla interest rate swaps. In a vanilla swap one exchanges the fixed swap rate against a floating LIBOR, which involves an interest rate relevant for that particular settlement period only. In a CMS swap this will be generalized. One will exchange the fixed legs against floating legs - usually the swap rate. In this note we give a new (for our knowledge) approximate formula for convexity adjustment based on forward measure approach and LIBOR market model. This link is interesting itself - showing that convexity adjustment is model and calibration dependent.