Hi skoh,
It's given in the answer, and it can be shown mathematically, but the idea is that, with respect to delta, dF/dS, the key difference between a futures and forward contract is the daily settlement: for the same movement in the spot price, for example $1.0 increase in the spot price, the present value of your forward gain is $1.0 because you wait for settlement, but the PV of the futures contract gain is slightly more at $1.0*exp(rT) because you settle that gain immediately.
From Answer to 17.21:
"The value of a forward contract on the asset is S0*EXP( -qT) – K*EXP(-rT). When there is a small change, ΔS, in S0 the value of the forward contract changes by EXP(-qT)* ΔS. The delta of
the forward contract is therefore EXP(-qT).
The futures price is S0*EXP((r-q)*T). When there is a small change, ΔS, in S0 the futures price change by ΔS*EXP((r-q)*T). Given the daily settlement procedures in futures contracts, this is also the immediate change in the wealth of the holder of the of the futures contract. The delta of the futures contract is therefore EXP((r-q)*T). The deltas of a futures and forward contract are not the same. The delta of the futures is greater than the delta of the corresponding forward by a factor of EXP(rT).
Please note that in regard to non-dividend-paying stock:
- Delta of forward = 1.0
- Delta of futures contract = EXP(rT)"
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