# Definition of Financial Futures: The value of a futures contract

According to the opening paragraph of the Wikipedia article for "Futures contract"

In finance, a futures contract (more colloquially, futures) is a standardized forward contract which can be easily traded between parties other than the two initial parties to the contract.

1. Does the delivery price change?
2. Does the contract have a non-zero value?
3. What happens to the margins accounts?

To elaborate, suppose at time $0$ I take a long position on a futures contract, $C$, on one unit of an underlying asset $A$ to be delivered on time $T >0$ for the delivery price of $P_0$. Suppose at time $0 < t < T$ I wish to sell $C$. It is my understanding from the quote cited above that it is possible to do so. Assume an arbitrage-free market with a constant zero risk-free interest rate.

1. Suppose at time $t$ the market quote for futures contracts on one unit of $A$ to be delivered at time $T$ is $P_t$. Which delivery price is the counter-party to whom I sell $C$ committed to? $P_0$ or $P_t$. In other words, suppose the counter party to whom I sell $C$ holds $C$ till the time of delivery. Are they required to pay out $P_0$ or $P_t$ in exchange of the underlying asset?

2. Is the counter party I sell $C$ to required to pay me for $C$? In other words, at time $t$ does $C$ have a non-zero value? We know that at the time of delivery, $C$ has a non-zero value, namely $S_A - P_0$, where $S_A$ is the value of $A$ at time $T$. This must be the case, since otherwise there is an arbitrage opportunity in the market. Indeed, if $C$'s value was naught at time $T$, a trader could buy $C$ for free and immediately parlay it for the underlying asset in exchange of $P_0$ for a net wealth increment of $P_0 - S_A$.

3. When I sell $C$ to the counter party at time $t$, what happens to my margin account? Does the counter party has to set up their own margin account? Does it matter if the exchange takes place before or after that day's end of trade time?

1. The new buyer is responsible for the price he agreed to i.e. $P_t$
3. Of course the other party has to have a margin account since as above, the futures contract essentially consists not of an "asset" you own but in daily marking to market and exchanging daily cash flows via the machinery of the futures exchange (margin accounts, the clearing house, etc.). The trade is cleared between you and the counterparty at the price $p_t$ you both agreed to (see question 1), the seller's account stops being credited/debited every day with variation margin and the process starts for the new "owner" of the contract.
I would add that because the contract is marked to market every day it's economic value is zero at the moment it is is so marked. Again, it is an agreement between you and the exchange to participate in a process of marking-to-market and possible delivery, not an asset with "value" that you "paid for". You may owe or be owed some money during the day but is paid out/taken away from you at night during the m2m (In particular I absolutely disagree that at maturity the contract is "worth" $P_A-S_0$ : much of that has already been paid or received by you through daily margin payments).
• Thanks. You wrote: "I absolutely disagree that at maturity the contract is "worth" $P_A−S_0$ : much of that has already been paid or received by you through daily margin payments" So What is the value of the futures contract just before delivery? – Evan Aad Mar 21 '16 at 14:33
• The remaining "value" just before expiry is $F (T-1,T)-F (T,T)$ which is most likely close to zero. – Quantuple Mar 21 '16 at 17:50