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  • 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 nat- ural martingale measure. As a typical example, the natural martingale measure of the swap rate is the swap measure with annuity as the nu- meraire. However, the evaluation of the discounted expectation of the payo® 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 nu- meraire change. We illustrate how the static replication of a CMS caplet by a portfolio of payer swaptions is related to convexity correction associ- ated 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. , Wendong Zheng and Yue Kuen Kwok (2010)
  • CMS Spread Options and Similar Options in Multi-Factor HJM Framework Constant maturity swaps (CMS), CMS spreads and similar products are analyzed in multi-factor HJM models. For Gaussian models, which include some Libor Market Models and the G2 model, explicit approximated formula are provided. The approximations are done through two different approaches: an exact solution to an approximated equation and an approximated solution to the exact equation. The first approach has been used previously in the literature for other models, the second is new. The approximations provide prices with error less than 0.02 basis point for the best approach; this is better than the previous literature and negligible in practice. The approach can be used to price standard CMS and CMS spreads and also for similar exotic products. , P.Hanton,M.P.A.Henrard (2010)
  • Saddlepoint Methods for Option Pricing , P.Carr, D.P.Madan (2008)
  • Juggling Snowballs , M.S. Joshi, C. Beveridge (2008)
  • Local Time for the SABR Model: Connection with the Complex Black Scholes and Application toCMS and Spread Options , E. Benhamou, O. Croissant (2008)
  • Callable Swaps, Snowballs and Video Games , C.Albanese (2007)
  • No-arbitrage conditions for cash-settled swaptions , F. Mercurio (2007)
  • Smile-consistent CMS adjustments in closed form: introducing the Vanna-Volga approach , F.Mercurio, M.Morini (2007)
  • Swaption Smile And CMS Adjustment , F.Mercurio (2006)
  • A stochastic volatility model for callable CMS swaps and translation invariant path dependent derivatives , C.Albanese, M.Trovato (2006)
  • Target Redemption Note , Y.Kuen Kwok, C.Chiu Chu (2006)
  • Swaption skews and convexity adjustments , F. Mercurio, A. Pallavicini (2005)
  • A Stochastic Volatility Model for Bermuda Swaptions and Callable CMS Swaps , C.Albanese, M.Trovato (2005)

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