# Call payoff diagram

## Video transcript

Payoff diagrams are a way of depicting what an option or set of options or options combined with other securities are worth at option expiration. What you do is you plot it based on the value of the underlying stock price. And I have two different plots here, one that you might see more in an academic setting or a textbook, and one that you might see more if you look up payoff diagrams on the internet, or people actually trading options. But they're very similar. This one just worries about the actual value of the options at expiration. This worries about the profit and loss. So this will incorporate what you paid for the option, this will not. This just says what it is worth. So with that said, we have company ABCD trading at 50 dollars per share, and then we have a call option with a $50 strike price or a$50 exercise price trading at $10. Which tells us that the owner of that option has the right but not the obligation to buy company ABCD stock at$50 per share up to expiration, assuming it's an American option. If it was a European option, it would be on expiration. So what is the value of this option at expiration? So this is value at expiration. So if the stock is worth less than $50, the owner wouldn't execute it, they wouldn't exercise the option. So the option would be worthless. It would be worthless. They would just let it expire. No reason to actually exercise the option. Now, if the underlying stock price is worth more than$50, if it's $51, then you would exercise it, because it's now-- the option is worth$1. You can buy something for $50 and sell it for$51, so it's now worth $1. If the underlying stock price is$60, of course, you would exercise it, it's now worth $10. Because you can buy something for$50, and you can immediately sell it at $60. We're saying that the underlying stock price is$60. So it would be worth $10. And so you have a payoff diagram that looks something like this. It kind of hockey sticks. Below$50, it's worthless, and then above $50, all of a sudden, it becomes worth something. Now, if you do it in the profit and loss model, all you have to do is incorporate what you actually paid for the option. So in this situation, below$50, you still would not actually exercise your option. Because why would you pay $50 for something that's actually trading for less than$50? But you would say, hey, I would have had to take a $10 loss, because I paid$10 for that option. So up until $50, your profit is negative$10. You have lost $10. You have lost the price of the option because you wouldn't exercise it. Then all of a sudden if the stock price goes above$50, you would exercise it, but you would still have a negative profit, because you still haven't made up the price of the option. All the way up until $60. At$60 per share for the underlying stock price, you could exercise the option, buy the stock at $50, sell it at$60. You would make $10 doing that, but, of course, you have to spend$10 on the option. So there you are break even. But then as you get above a \$60 stock price at maturity, then all of a sudden you start to make money. So these are both legitimate payoff diagrams for a call option, for this call option right over here. They're just different ways of viewing it. This is the value of the option. This incorporates the actual cost of it.