On the valuation of constant maturity swaps

This research aims to develop a valuation technique for constant maturity swaps (CMS) based on convexity corrections. We explicitly incorporates into our valuation model both 1) complex shift patterns of the yield curve and 2) implied volatility smile and skew effects. The method requires numerically integrating an infinite string of European swaptions across all strikes induced by the stochastic volatility model calibrated to the market. Numerical experiments demonstrate validity and instrumentality of our proposed method