Convexity meets replication: Hedging of swap derivatives and annuity options

Convexity correction arises when one computes the expected value of an interest rate index under a probability measure other than its own natural martingale measure. As a typical example, the natural martingale measure of the swap rate is the swap measure with annuity as the numeraire. However, the evaluation of the discounted expectation of the payoff in a constant maturity swap (CMS) derivative is performed under the forward measure corresponding to the payment date. In this study, we propose a generalization of the static replication formula by exploring the linkage between replication, convexity correction, and numeraire change. We illustrate how the static replication of a CMS caplet by a portfolio of payer swaptions is related to convexity correction associated with the bond–annuity numeraire ratio. We also demonstrate the use of the generalized static replication approach for hedging the in‐arrears clean index principal swaps and annuity options © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:659–678, 2011