Rewrite the expression for the swap rate from the previous question in terms of a weighted sum over FRA rates spanning the swap period, i.e.

where Tα ≤ t

using the abbreviation τi = τ(Ti−1, Ti). Now, assuming that the variability of the weights is much smaller than the variability of the FRA’s derive an expression for the quadratic variation of the swap rate at time Tα evolved from T = 0 (this is the Rebonato formula quoted in (7.17)).

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== B Sas(t) = w(t)Fi(t) i=a+1