Post by alanbond on Jul 28, 2009 8:28:59 GMT 4
Convexity Meets Replication: Hedging of Swap Derivatives and Annuity Options
Wendong Zheng
Yue Kuen Kwok
Hong Kong University of Science & Technology - Department of Mathematics
June 18, 2009
Abstract:
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 paper, we propose an extension of Carr-Madan's static replication approach 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 extended static replication approach for hedging in-arrears clean index principal swaps and annuity options.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1421734_code384844.pdf?abstractid=1421734&mirid=4
Wendong Zheng
Yue Kuen Kwok
Hong Kong University of Science & Technology - Department of Mathematics
June 18, 2009
Abstract:
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 paper, we propose an extension of Carr-Madan's static replication approach 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 extended static replication approach for hedging in-arrears clean index principal swaps and annuity options.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1421734_code384844.pdf?abstractid=1421734&mirid=4