Futures Daily Settlement and the Difference from Forwards

Summary

The document explains that taking a futures position does not mean receiving its quoted price immediately. Futures are marked to market through daily margin payments, which reset the position’s net present value to zero each day. By contrast, a forward contract generally settles at maturity. Thus, even if a futures price is negative, the price is not an immediate cash payment to a new long position; gains and losses are transferred through settlement over the contract’s life.

It also describes how this settlement convention affects valuation. Forward and futures prices can correspond to expectations under different measures, and their values may differ when interest rates covary with the underlying asset. With deterministic rates, or rates uncorrelated with the underlying, the expectations coincide and there is no convexity adjustment. The account assumes standard margining and gives no treatment of exchange-specific settlement rules, margin mechanics, or delivery details.

Key ideas

• A forward typically exchanges cash at maturity, while a future settles gains and losses through daily margining.
• Daily settlement resets the futures position’s net present value to zero.
• A negative futures quote is not paid to a new long trader immediately as the contract price.
• Futures and forwards can differ in value because their valuation uses different probability measures.
• The convexity adjustment disappears when rates are deterministic or uncorrelated with the underlying.

Tags

# At some intermediate time $t$, does money actually change hands in the trading of a futures contract?


# At some intermediate time $t$, does money actually change hands in the trading of a futures contract?












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 $T$?

## Answer by Antoine Conze (score 3, accepted)

https://quant.stackexchange.com/a/38079

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.