For a stock that does not pay dividends, which of the following represents the delta of a futures contract?

For a stock that does not pay dividends, which of the following represents the delta of a futures contract?
A . 0
B . e^(rt)
C . 1
D . Futures contracts do not have a delta as they are not options

View Answer

Answer: B

Explanation:

The delivery price of a futures contract is given by Se^(rt), just as in the case of a forward contract. However, a key difference is that a forward is settled at maturity whereas a futures contract pays out the P&L daily. So if the spot price increases from S to S, the holder of a futures contract immediately receives the change in the delivery price without any discounting to the present. That is, the holder of the futures contract receives (S + S)e^(rt) – Se^(rt) = Se^(rt) right away. Therefore the delta of a futures contract is e^rt, which given positive non-zero values of r and t can only be greater than zero.

Therefore Choice ‘b’ is the correct answer. Note the difference from a forward contract where this difference is not received till the delivery date, therefore making the delta of the forward contract to be equal to 1.