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To Problem 2.22 in Options, Futures, and Other Derivatives (8th edition) below:

When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one." Explain this statement.

the Solution is:

If both sides of the transaction are entering into a new contract, the open interest increases by one. If both sides of the transaction are closing out existing positions, the open interest decreases by one. If one party is entering into a new contract and the other party is closing out an existing position, the open interest stays the same.

I can understand the "increases by one" case but have difficulty in understanding the latter two cases, probably I did not fully understand the "closing out" process. By my understanding, "closing out" means "executing a reversing transaction that is exactly the same as his original trade" and "the positions is usually closed out by entering into a new arrangement with another party" (source). Therefore, "closing out the existing position" does not necessarily imply that the original contract is gone (hence "decreases the open interest by one").

To be more specific, let $A$ and $B$ denote the two parties that traded the new futures contract $x$. Suppose $A$'s existing position is the long position of contract $y$, and $B$'s existing position is the short position of contract $z$. Here both $y$ and $z$ were settled prior to the time that $x$ was settled, which is denoted by $t$. By assumption, $x, y, z$ have the same maturity time $T > t$. In addition, at $t$, $A$ shorts $x$ and $B$ longs $x$. Under this setting, the number of long positions did not decrease by one, but increases by one (in addition to $y$, there is a new outstanding $x$).

Where did I my understanding go wrong?

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There seems to some confusion about the language. The book is referring to trades that are all on the same futures contract , just done at different times and different prices. So when it says ‘new contract’ it should really say ‘new trade on the same contract ‘. Then it should become obvious. If you are long 1 contract of the TYH3 for example , then you enter into a new trade where you sell one contract later at a different price, you have closed out your position. Now when you sell a futures contract, there is some participant in the other side who buys it. If that person is also closing out a position, the open interest has decreased. If that person is entering a new long, then the effect is just to transfer your long to someone else, so there is no change in open interest. Does this help. ?

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  • $\begingroup$ Thanks for your answer, dm63. To clarify, should "there is some participant in the other side who sells it" be "there is some participant in the other side who buys it"? $\endgroup$
    – Zhanxiong
    Dec 8, 2022 at 15:10
  • $\begingroup$ The confusion that I am still having is: what is the status of my original counterparty B as I closed out my position by entering a trade with a new counterparty C? I think the original contract was still held by B and continue to exist? @nbbo2's answer below seems easier to follow in this regard, is his answer essentially the same as yours? $\endgroup$
    – Zhanxiong
    Dec 8, 2022 at 15:16
  • $\begingroup$ Yes apologies on the first comment I will edit $\endgroup$
    – dm63
    Dec 9, 2022 at 3:44
  • $\begingroup$ Yes the original contract of B continues to exist $\endgroup$
    – dm63
    Dec 9, 2022 at 3:47
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    $\begingroup$ This is correct. As long as you understand that each transaction is done on the exchange - you never actually know who is the other side , only the exchange can see that. $\endgroup$
    – dm63
    Dec 15, 2022 at 12:03
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@dm63 answer is correct, I just wanted to add some details that helped me when I first started learning about Open Interest (OI). I think it was also helpful to also look at Volume at the same time.

OI is defined as the total number of contracts (listed option or futures) that have not been closed (offset), liquidated, or delivered. With this definition, each transaction can affect OI in one of 3 ways

• Increases
• Decreases
• Remains unchanged

Volume on the other hand starts every day from zero and counts every transaction.

The below is a simple illustration of the impact on OI and volume for trades during a single session: enter image description here

  • The first and second examples should be clear.
  • The third reduces OI because the transaction closes out existing contracts of A and D.
  • The fourth is the one you seem to have trouble with. To best understand this (as well as the third example), you need to understand how delivery works.

The following graphic from the CME shows that in the central counterparty clearing model, CME clearing confirms, clears and settles all CME Group trades.

enter image description here

It also regulates delivery, among other things. Cash settlement is easy to understand, because it is just dollar payments that need to be distributed correctly. Physical settlement is the tricky part and I suggest reading any contract's details on the respective website for the specifics. In the example of CME lumber, all participants with remaining long and short positions will be matched with an emphasis on keeping size together for Exchange delivery. Once matches are made, the party providing shipping instructions has two business days to do so. Therefore, the contracts do not need to have the same counterparties over time. If B "lost" A, it will just be matched to someone else (if B does not close out prior to expiry as well).

This link desribes the delivery of US treaury futures (most importing for your purpose is the section: "The role of the clearing firm").

The same logic applies to any exchange. Hope this helps.

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  • $\begingroup$ Thank you very much for the answer, AKdemy. The reference you mentioned is also very helpful. Just one more thing: in your example (3rd row), if A closed out its position in the contract with B, does that imply that B automatically become a counterparty to C, whose original counterparty was D? If not, did B and A get their new counterparties (I suspect no, for which the OI will remain the same instead of decreasing by $1$)? $\endgroup$
    – Zhanxiong
    Dec 14, 2022 at 4:37
  • $\begingroup$ If no other transaction will happen, B will be matched with C (both have one contract left), and D will be matched with E (both have two). $\endgroup$
    – AKdemy
    Dec 14, 2022 at 7:01
  • $\begingroup$ I see. To clarify, my comment above regards the 3rd row of your example only, while your reply seems to have included the 4th row too. But I think I got what you meant and we are in agreement. $\endgroup$
    – Zhanxiong
    Dec 14, 2022 at 13:42

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