Convexity Adjustments and Forward Libor Model: Case of Constant Maturity Swaps

We investigate the theoretical and empirical difference between thestandard convexity adjustment and Forward Libor Model in a particular case oftwo-period Constant Maturity Swaps. Using daily data from 1991 to 1997, wesimulate the difference (spread) between the two-period CMS swap rates calcu-lated by convexity adjustment and Forward Libor Model. The spread reaches8.49 basis points in some cases, and correlation coeffcients between spread andone-year, two-year cap volatilities are 0.8750 and 0.7939, respectively. Moreover,convexity adjustment yields CMS swap rates higher than Forward Libor Modeldoes. Since the pricing using Forward Libor Model would be exact, we concludethat the convexity adjustment overestimates CMS swap rates. In this paper, wesimulate two-period CMS swap, and it is reasonable to believe that the spreadwill be much bigger for longer period CMS swap or other convex instrument.