Convexity meets replication: Hedging of swap derivatives and annuity options
研究了凸性修正与静态复制的关系，提出广义静态复制公式，用于对冲固定期限互换（CMS）衍生品和年金期权，对金融工程和风险管理从业者有参考价值。
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