A call option gives the buyer the right, but not the obligation, to purchase a stock at the call option's strike price on or before the contract's expiration date. When you buy a call, you go long and have the "option" of buying the underlying stock at the option's strike price. You do not have to exercise this option, however. Instead, you also have the right to close your long call position by selling it in the open market.
To understand if you can sell call options you purchased, you must first wrap your head around basic options terminology. When you "buy to open" a call option, you give yourself the right to purchase the underlying stock at the option's strike price on or before the contract's expiration day. For instance, if you buy a $15 call option on stock XYZ with an August expiration, you can exercise your option to buy 100 shares of the stock for each option contract you own at $15 per share on or before the August options expiration date.
Sell to Close
As the owner of a call option, you can elect not to exercise your option to buy the underlying stock. In most cases, investors who do not exercise their option sell it. When you do this, you "sell to close" your position. In this case, you have sold a call option that you originally purchased.
Profit or Loss
Just like when buying and selling shares of stock, you realize a profit or loss when you sell to close a call option contract. When you purchase a call, you pay a premium for the right to buy the underlying security. Depending upon the movement of the underlying stock, you can sell the call position to close prior to option expiration day for a premium that is either higher or lower than your purchase price. Many factors, including how much time remains until options expiration day (time decay), impact the price.
As the Chicago Board Options Exchange website explains, options contracts can expire worthless. Generally, if you own a call option that is "in-the-money" (the market price of the underlying stock at expiration is higher than the option's strike price), your broker will exercise the option for you and you will purchase 100 shares of the underlying stock for each contract you own. If, however, the option is out-of-the-money at expiration and you have not sold to close your position, it will expire worthless. This simply means that the option no longer has value and you will lose the entire amount of your original investment.