Payoff diagrams are a way of depicting what option or set of options or options combined with other securities are worth at option expiration.
What you do is plot it based on the value on 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 people actually trading options.
But they're very similar; this one just worries about the actual value of the options at expirations and this worries about the profit and loss.
So this one will incorporate what you paid for the option, this will not. This just says what it is worth.
WIth that said, we have company ABCD trading at $50 per share. And 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 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 the $50, if its $51 then you would exercise it, because now the option is worth $1. You can buy something for $50 and now sell it for $51.
So its now worth $1. If the underlying stock price is $60, of course you would exercise it [as] its 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: a kind of hockey sticks.
Below $50 its 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 loss because I paid $10 for that option"
So up until $50 your profit is -$10, you have lost $10 dollars, 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 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 had to spend $10 on the option so there you would break even.
But then as you get above a $60 stock price at majority, 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 options, this incorporates the actual cost of it.
We have company ABCD trading at $50 a share
Let's draw a payoff diagram for a put option
with a $50 strike price trading at $10
So once again we get to draw two types of payoff diagrams
One type that only cares about the value of
the option at expiration.
This is what you tend to see in academic settings
like business schools or textbooks.
And the other one will actually draw a profit
and loss based-on that option position,
so incorporate the price you actually paid for the option.
You tend to see this more in practice.
So you have a put option.
Remember, this is the right to sell the stock at $50.
So the stock let's say at expiration.
All of these are at expiration.
At expiration the stock is trading at $0,
the company went bankrupt.
Now it's worthless. What is the put option worth?
You would now go on the market, buy it for almost $0 ,
and then you would exercise your put option
and then you would sell it for $50.
So you would definitely excerise it,
and you'd make a lot of money the underlying stock
can be bought for $0,
the put option is now worth $50,
because you can buy it for 0 and sell it for 50 dollars.
if you have the put option.
If the underlying stock price is $10,
then you could still go to buy the stock for $10.
If you had the option,
you would excercise the option to sell it for $50,
so you would make $40.
So, the option would be worth $40.
And anyone who's holding the option would make instant $40.
So, the value of the option becomes less and less,
as the value of the stock becomes more and more,
up until you you get to $50.
At $50 you wouldn't really care
you have the right to sell something at $50,
which you could buy for $50.
So, it's kinda worth nothing.
The value of the put option could start at $50,
because you have the right to
sell something worthless at $50,
if the stock's going bankrupt
After $50, it becomes the option.
You don't really doesn't have any value anymore.
And if the stock goes anything above %50,
it's still worthless.
If the stock is $100 or something like that,
there's no way you could exercise the option.
because why would you excercise the right to
sell something at $50,
while in the open market you can sell it at $100.
Let's do the same thing for the profit/loss version.
So, the stock is worth nothing,
you can buy it for nothing,
and then if you have the option, sell it for $50.
But, we have to incorporate the fact that
you paid 10 dollars for the option.
So, instead of the option is worth $50,
we would say it's worth 50 minus this
So, it'd be worth $40.
And this is all the way you would exercise the option
all the way until the option is worth $50
But at $50, instead of saying it's worthless,
you have to remember, if the stock is 50$,
you wouldn't exercise the option.
But you did pay $10 for it.
So, you wouldn't exercise something that you paid $10 for
so you would have to take a $10 loss.
so the option started at 50,
and it'd become less and less,
all the way to the point that if you don't exercise it,
you would took the loss of paying for the option.
not exercising it.
And any stock price above that,
you just took a $10 loss.
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