Exercise price
The exercise price is the fixed price written into an options contract at which the buyer of that contract can buy or sell the underlying stock, if they choose to use the option. It is also called the strike price, and the two terms mean exactly the same thing on listed (exchange-traded) options.
An option is a contract that gives its buyer the right, but not the obligation, to buy or sell 100 shares (typically) of a stock at a specific price, by or on a certain date. That specific price is the exercise price. If you hold a call option, the exercise price is what you'd pay to buy the shares. If you hold a put option, it's what you'd receive for selling the shares. The price is set when the option is created and does not change for the life of that contract, no matter where the actual stock price moves.
The nuance beginners trip over is that the exercise price has nothing to do with what you paid for the option itself. The cost of the option contract is the premium, a separate, usually much smaller number that fluctuates with time, volatility, and how close the stock price is to the exercise price. A call with a $50 exercise price might cost $2.30 per share as a premium; exercising it means paying the $50, not the $2.30, to actually acquire the stock.
Whether exercising is worthwhile depends on where the stock is trading relative to the exercise price. A call is only worth exercising if the stock is trading above the exercise price; a put is only worth exercising if the stock is trading below it. Most short-term option traders never exercise at all — they buy and sell the contracts themselves and let the changing premium do the work.
Day traders working with options need the exercise price to judge how far the stock has to move for a position to have real intrinsic value, and to pick strikes that match how much movement they're actually expecting in a session.
Suppose a stock is trading at $48 and you buy a call option with a $50 exercise price for a premium of $1.10 per share. If the stock rallies to $53 before expiration, exercising the call lets you buy shares at $50 that are worth $53, a $3 gain per share before accounting for the $1.10 you paid. If instead the stock stays at $47, there's no reason to exercise — buying at $50 would cost more than the stock is worth on the open market — and the option would simply expire worthless.
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