Now I am reading the paper: "Swaption skews and convexity adjustments" by Mercurio and Pallavicini,2006. Where they adjust the standard convexity adjustment when a smile of swaption is present. The conclude the convexity adjustment is completely determined by to smile of swaption. They link the standard convexity adjustment to the smile of swaption smile by the a static replication at page 4. I can not understand the static replication strategy they implement at page 4 where they say, when static augment is implemented, the second moment of the CMS rate become

maybe expanding and applying symmetry arguments toworksI tried but couldnot work it outMaybe you will do better,will try again later

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