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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.