Delivery Timing and Pricing of Futures Contracts
Summary
The discussion clarifies why a futures contract with a delivery window cannot be treated like a contract with one fixed expiry date. The standard cost-of-carry relationship assumes a single delivery date. When delivery can begin before the final delivery deadline, the date itself affects the contract’s value and becomes part of the analysis. Bond futures are given as an example of contracts with a delivery period.
The response describes delivery option analysis as a way to handle this timing choice. Some traders avoid the period when delivery may occur, while others use optimization models; before the delivery window opens, the cited approach assumes delivery occurs at the date least favorable to the trader’s position. A second answer emphasizes that early physical settlement is governed by contract rules and may entail storage costs. The comments rebut the suggested arbitrage, but provide no detailed model or contract-specific rule, so actual terms must be checked for each futures market.
Key ideas
- A delivery window makes the delivery date a pricing variable.
- The single-date cost-of-carry formula does not capture delivery timing options.
- Delivery option analysis addresses the uncertainty over when delivery will occur.
- Some traders avoid the delivery window, while others model its timing explicitly.
- Physical settlement timing and associated costs depend on the contract’s rules.
Tags
Full text
# Deliver Futures before last trading day
# Deliver Futures before last trading day
I found that for the exchange traded Futures, we can deliver the Futures before the last trading day, namely you can sell a Future then deliver it immediately, which definitely has a arbitrage opportunity if spot price and Future price are different.
So do I misunderstand some rules of exchanged Futures?
## Answer by nbbo2 (score 2)
https://quant.stackexchange.com/a/54306
If a Futures contract has two separate dates $T_d$ (when deliveries may begin) and $T_f$ (which is the last date by which delivery must take place) then you cannot use the formula found in introductory books such as Hull:
$$F=S e^{rT}$$
For example for Bond Futures $T_d$ is about one month before $T_f$. In that case which value of T would you use? The formula has been derived under the assumption of a single delivery date (which is true for example for Stock Index Futures).
For such cases the choice of the delivery date itself becomes a variable in the problem, and there are various (complicated) theories and methods available (generally described as Delivery Option analysis). Markets participants are certainly aware that the delivery date is uncertain for these kinds of futures; some (such as myself) simply avoid trading the future between $T_d$ and $T_f$ when the delivery may take place, and leave the "delivery timing game" to the specialists. Between time 0 and $T_d$ they assume delivery will take place at whichever of $T_d$ or $T_f$ is least favorable for their position. Others use much more complex optimization models.
But yes, real world futures can be more challenging that those presented in introductory courses.
## Answer by ThatDataGuy (score 0)
https://quant.stackexchange.com/a/53486
You can't "deliver" a futures contract. Its not a thing - it is a legal contract with the exchange.
A physically settled futures contract cannot be physically settled early unless the rules permit it. Think about it - you can't turn up early and dump loads of stuff at the delivery point early and say you are done. Storing it until the delivery date will cost money. The warehouse owner will charge you, etc. And you can't say that the exchange owns it, because until the delivery date, legally they don't. You could disown it, but then the warehouse will sell it on the spot market and keep the proceeeds.
So in short, there is no arbitrage opportunity in this respect.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.