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Buying a put option gives you the right to sell the specific financial instrument underlying the option at a specific price, called the exercise or strike price, to the writer, or seller, of the option before the option expires.
You pay the seller a premium for the option, and if you exercise your right to sell, the seller must buy.
Selling a put option means you collect a premium at the time of sale. But you must buy the option's underlying instrument if the option buyer exercises the option and you are assigned to meet the contract's terms.
Not surprisingly, buyers and sellers have different goals. Buyers hope that the price of the underlying instrument drops so they can sell at the exercise price, which is higher than the market price. This way, they could offset the price of the premium, and hopefully make a profit as well.
Sellers, on the other hand, hope that the price stays the same or increases, so they can keep the premium they've collected and not have to lay out money to buy.