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Open interest (also known as open contracts or open commitments) refers to the total number of outstanding derivative contracts that have not been settled (offset by delivery).
For each buyer of a futures contract there must be a seller. From the time the buyer or seller opens the contract until the counter-party closes it, that contract is considered 'open'.
Open interest also gives key information regarding the liquidity of an option. If there is no open interest for an option, there is no secondary market for that option. When options have large open interest, they have a large number of buyers and sellers. An active secondary market will increase the odds of getting option orders filled at good prices. All other things being equal, the larger the open interest, the easier it will be to trade that option at a reasonable spread between the bid and ask.