A covered call is a financial market transaction in which the seller of call options owns the corresponding amount of the underlying instrument, such as shares of a stock or other securities. If a trader buys the underlying instrument at the same time the trader sells the call, the strategy is often called a "buy-write" strategy. In equilibrium, the strategy has the same payoffs as writing a put option.
The long position in the underlying instrument is said to provide the "cover" as the shares can be delivered to the buyer of the call if the buyer decides to exercise.
Writing (i.e. selling) a call generates income in the form of the premium paid by the option buyer. And if the stock price remains stable or increases, then the writer will be able to keep this income as a profit, even though the profit may have been higher if no call were written. The risk of stock ownership is not eliminated. If the stock price declines, then the net position will likely lose money.Since in equilibrium the payoffs on the covered call position is the same as a short put position, the price (or premium) should be the same as the premium of the short put or naked put.