For a cash-settled swaption, the cash-annuity is defined by This is j ust some function of R

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For a cash-settled swaption, the cash-annuity is defined by Ac(RT) = 1 N 1 (1+ RT )ni n This is j ust some function of RT. Do a second order Taylor-expansion of Ac(RT) about Ro. Notice that under the T-forward measure, we get Et [Ac(RT)] ≈ Ac (R0). Further, assume that the swap rate follows a lognormal process, i.e. dRt = σRtdWt. Hence, show that Et [RT] ≈ RRTA(Ro) A(Ro) gives the classical approximation for the CMS rate in the (skewless) lognormal world.

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