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Assuming that the asset underlying a futures contract pays no dividends or associated (storage, etc) costs, I have the following formula for the price $F_t$ of a futures contract at time $t$: $$ F_t = S_t \cdot e^{r (T-t)} $$ where $S_t$ is the value of the underlying asset at time $t$, $r$ is the risk-free rate, and $T$ is the contracts delivery date.

Suppose that $F_t < 0$. If I were to take a long position on this contract at time $t$ in a real world situation, would I immediately receive the amount $F_t$, or would all money change hands only at delivery time $T$?

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    $\begingroup$ Note that $S_t$ is $\ge 0$ and consequently so is $F_t$ $\endgroup$ – noob2 Feb 5 '18 at 15:06
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Forward contract: exchange is done at maturity.

Future contract: margin call is paid/received every day throughout the life of the contract, thus resetting the NPV of the position to zero every day.

This explains why $F^{\text{forward}}_t=E^{Q^T}_t[S_T]$ and $F^{\text{future}}_t=E^{P}_t[S_T]$ where $Q^T$ is the $T$-forward measure and $P$ is the savings account risk neutral measure. When rates are deterministic (or uncorrelated to the underlying) $E^{P}_t[S_T] = E^{Q^T}_t[S_T]$ (no convexity adjustment).

You can also view the future contract as being a perfectly collateralized forward contract with a rate of remuneration of zero on the collateral.

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