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You offset an options or futures position by taking a second position in a contract with identical terms, buying if you sold initially or selling if you bought initially.
With the offset, you neutralize any potential obligation you had to fulfill the terms of the contract, and you may make a profit or reduce a loss with the transaction.
For example, if you'd sold an equity call option that is close to being in-the-money, you might buy an offsetting call option. That neutralizes your obligation to deliver the underlying stock if the option you sold is exercised.
In a tax context, you can use capital losses to offset an equivalent dollar amount of capital gains, or up to $3,000 in capital losses to offset ordinary income. In either case, the offset allows you to reduce the tax you owe.
Further, banks have the right of offset if a borrower defaults on a loan. That right allows a bank to seize assets in the borrower's deposit accounts with the bank to reduce or eliminate any loss on the loan.