Yes. Options can be sold without you owning them but this is not known as short selling. When you buy an option, you pay out money to someone and obtain the right to buy (or sell, in the case of put options) the underlying at the strike price. The seller of the option sells you this right to buy (or sell) the underlying at the strike price and in return for a premium. The seller therefore takes money in, but also takes on the obligations that go along with the contract.