Put writer payoff diagrams - Economics Video Lecture

If I were to buy a put option with a fifty dollar excercise price
and if I were to buy it for $10.00, then the value of my position
the payoff for that put option, at the maturity
or at the expiration I should say. At the expiration of the option.
Depending on what the stock price is, and expiration would look like this:
if the stock price is worth, if the stock price goes to zero
then the put option is worth fifty
because I could buy the stock at zero
and excercise my option
to sell at fifty. At "putting" the stock to someone else
at fifty dollars. All the way to if the stock becomes worth fifty
then my put option, I wouldn't need to excercise it
because why would I?
It's worthless to have the option to sell something at fifty
where you can just sell the actual stock in the open market
or buy the stock at fifty. So then the put option becomes worthless
for a stock price above that.
Now, this is the payoff diagram.
And this is when we just think about the value and expiration.
If we think about the actual profit and loss at expiration, it would look like this
It would just be shifted down by ten dollars
because we have to pay $10 to get this value.
So if the stock is worth zero, the put option is worth
$50, but I spent $10 dollars to get it, so the profit is going to be
$40 dollars.
And so then at $50, I wouldn't excercise the put option
so I've lost the $10 dollars I spent on the option
so my payoff diagram would look like, I'm gonna draw it,
relatively neatly. My payoff diagram would look like this
Once again, this payoff diagram just incorporates the price of the option
So it's the actual profit. This is just the value at expiration,
depending upon what the value of the stock is at expiration.
Now this is just a situation if you were to buy an option
but there has to be someone on the other side of the contract
someone who's holding, agreeing to buy the option for you
So you could actually have the writer, you could actually have the writer, of the put
the payoff diagram we just showed is the person who owns the put,
but someone else had to have created the put.
They said, "Oh, you know what, I will give you the right.
"I will give you the right to sell, to sell me the stock at $50, up to some expiration date."
So what does their payoff diagram look like?
Well if this guy is going to be able to make $50, this guy over here
the writer of the put, the writer of the put
is going to lose $50. He's going to have to essentially go out
he's actually going to have to buy that $50 put or buy that $50 stock from this person
because he has to uphold his side of the transaction
but he's buying something for $50 that's worthless
because based over, at this end of the axis, the stock would be worth nothing
so he's taking a $50 loss, all the way to him not having to do anything
because the put holder won't actually excercise their options
if their stock price is $50, so their payoff diagram is going to look like this
So you can see it's actually the mirror image
of the payoff diagram of this person on the other side of the contract
And if you were to add these two payoff diagrams, you would be neutral,
because all of the money is exchanging hands between the buyer
and the seller of the put.
If you look at the actual profit or loss
if the put is not excercised
then the writer of the put essentially just got a free $10
He sold the put, he sold the put to this guy for $10
He created the put and sold it to that guy for $10
the put is not excercised, he gets to keep that $10.
But then if the stock goes down and he's forced to buy the stock
from the owner of the put
he has to buy it because that's his side of the deal
then all of a sudden he loses money
So he would go, if all the way down if the stock is worth nothing,
He is forced to buy something for $50 that is worth nothing
He would take a $50 loss, but he paid the $10 on the actual price of the option
so it would be a negative $40 profit
So his profit and loss would look like this
But once again, these are the mirror images of each other.