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The futures convexity correction is a number that is used in the process of implying a futures price out of a given yield curve.
It is actually a correction added on the respective implied forward rate, so that a typical futures convexity correction would be a number much smaller than that forward rate, e.g. 0.001 when the forward rate would be 0.04
More specifically, when the yield curve is known, then all discount factors - for all future maturities - are known.
It turns out, that all forward rates are also known, due to the formula r = (DF1/DF2 - 1)/(T2-T1) for any forward rate r between times T1 and T2.
Unfortunately the corresponding futures rate f must generally differ from the forward rate due to the fact that f reflects the cost of a "futures contract", which differs from a "forward contract" in that it involves daily "mark to market".
One simple approach to account for this "mark to market" effect is to assume the formula f = r + c, where c is an ad-hoc fixed number called futures convexity correction.
Therefore provided the number c is known for each pair of times T1 and T2, the futures rate f can be then implied out of a given yield curve.
Finally the corresponding futures price F is defined by F := 100(1-f)