Pay-off diagrams are a way of depicting what an option or a 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 plot types here. One that you might see more in an academic setting or a text book

and one that you might see more if you look up pay-off diagrams on the internet or people actually trading options.

But they are 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 per share. Then we have a call option with a $50 strike price or $50 exercise price

trading at $10 which tells us that the owner of that option has the rigth, but not the obligation, to

buy company ABCD stock at $50 per share up to expiration, assuming it is 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 it's value at expiration, 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 is $51 then you would exercise it

because now the option is worth one dollar, you can buy something for $50 and sell it for $51 so it is now worth

one dollar. If the underlying stock price is $60 of course you would exercise it and now is worth $10 because you can buy something for 50 and you could immediately sell it at 60.

We are saying that the underlying stock price is 60 so it would be worth 10. So you have a pay-off diagram

that looks something like this. It kind of "hockey-sticks", below 50 it is 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 is actually

trading for less than $50? But you would say, hey, I would have had to take a $10 dollar 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 the stock price goes above

$50 you would exercise it but you 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 had to spend $10 on the option. So there you are break-even. But then you get 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

pay-off diagrams for a call option, for this call option right over here.

There are just different ways of doing it. This is the value of the option, this incorporates the actual cost of it.