July 16th, 2004, 6:11 pm
Suppose on will recieve the floating leg and pay the fixed leg of a swap which begins in 5 years and lasts, say, 10 years. Suppose the relevent swap rate (10y rate, five years forward) goes up. Then the (forward) value of the swap does not go up proportionally because as rates go up, the discounting of the payments increases. Similarly, as rates go down the (forward) value of the swap does not go down proportionally because as rates decrease, the discounting is less severe. Since a swap is a readily tradeable instrument, on average the (forward) value of the swap does not change. Therefore the swap rate itself must have a drift term. This drift term is the convexity correction of the CMS deal