Convexity Without Replication

We revise the standard analysis of constant maturity swaps, caps, and floors to account for dual forecast and discount curves. This reduces the pricing of these deals to evaluation of quadratic swaplets, caplets, and floorlets. We use the explicit, closed-form expressions for the value of these quadratic options under the SABR model. This enables us to use swaption smile information to improve CMS pricing, without resorting to onerous numerical replication techniques. We extend this analysis to obtain the convexity corrections for Libor-in-arrears and other mis-matched simple rates, and to value IRR-settled swaps and swaptions.