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 $T$?

  • 2
    $\begingroup$ Note that $S_t$ is $\ge 0$ and consequently so is $F_t$ $\endgroup$
    – nbbo2
    Feb 5, 2018 at 15:06

1 Answer 1


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.