Hi
@[email protected] I've struggled with this in the past; e,g, here is a nine-year old thread where I am not sure that I make any sense
https://www.bionicturtle.com/forum/threads/delta-of-forward-and-future.336/
But i wonder why i've never considered this simply, where Hull distinguished between forward value and futures price
- the value of a forward contract, f = [F(0) - K]*exp(-rt) where F(0) = S(0)*exp(rT) such that f = [S(0)*exp(rT) - K]*exp(-rt) = 1.0*S(0) - K*exp(-rT) and ∂f/∂S = 1.0; ie, K is constant
- the price of a futures contract per cost of carry, F(0) = S*exp(rT) where ∂f/∂S = exp(rT).
I think given time I could actually connect this to the fundamental narrative explanation for the difference (which is that the futures contract settles daily which creates cash in-flow/outflow at the margin--literally via the margin account), along the lines of: the forward contract future value is discounted back, which negates the risk free growth; but the futures contract price is immediately responsive to riskfree rate changes, or put another way, unlike the forward math, effectively it is
not getting nullified by not being discounted back, which is economically similar to investing now at that risk free rate (and earning the gain). My phrasing could stand much improvement, hopefully this makes a bit of sense ... thanks,
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