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

## Question:

For a cash-settled swaption, the cash-annuity is defined by This is j ust some function of R_{T}. Do a second order Taylor-expansion of A_{c}(R_{T}) about Ro. Notice that under the T-forward measure, we get Et [A_{c}(R_{T})] ≈ A_{c} (R_{0}). Further, assume that the swap rate follows a lognormal process, i.e. dR_{t} = σR_{t}dW_{t}. Hence, show that Et [R_{T}] ≈ R_{0 }− gives the classical approximation for the CMS rate in the (skewless) lognormal world.

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