Convexity meets replication: Hedging of swap derivatives and annuity options
✍ Scribed by Wendong Zheng; Yue Kuen Kwok
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 158 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0270-7314
No coin nor oath required. For personal study only.
✦ Synopsis
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