# How much amount is tranferred in market to market settlement of futures?

The book by J.C. Hull gives a proof that if interest rate is constant, futures price is same as forward price (no-arbitrage price).

In the proof outlined in the book, scenario of daily settlement is taken. The buyer enteres into a long futures position on end of day 0 and the future expires on day `N`. At the end of day `1` the settlement is `F_1 - F_0` (where `F_i` is future price at the end of day `i`). Similarly for other days `F_i - F_{i-1}`.

My question is to make the value of futures contract zero at the end of day 1, shouldn't `(F_1 - F_0)*e^{-r(N-1)}` ie. the present value (`r` is continuously compounded constant interest rate with time in days) be the settlement at the end of day `1`, as that is what the value of a forward contract would be on the end of day `1` (having same maturity date and negotiated at end of day `0`).

• "My question is to make the value of futures contract zero at the end of day 1" This doesn't seem to make much sense. Can you elaborate / clarify? – ThatDataGuy Jan 6 '20 at 16:25