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Say stock XYZ is trading at 31 dollars.
We have a call option on XYZ with a $35 strike price.
It's trading at $8.
We have a put option on XYZ with a $35 strike price,
they have the same strike price,
trading at $12, and they both have the same
expiration over here,
and finally there's a bond, unrelated to XYZ.
It's going to be a risk free bond, like a treasury bill
worth $35 at option expiration
and you can buy it right now at $30.
The reason you can get it for less is you're going
to get $35 in the future at option expiration
so you're essentially getting interest on that bond
So with these numbers, is there a way to make
risk-free money?
To think about that, let's think about
the put-call parity. We learned
that a stock plus a put at a given strike price
the put is a put on that stock
is equal to, is going to have the same value
at expiration as a call with the same strike price
with the same underlying stock
plus a bond, a risk-free bond, that's going
to be worth that strike price at the expiration
of these two options.
Since this is going to have the same value,
the same payoff,
in any circumstance, as this at expiration
they really should be worth the same thing
but when you look at the numbers over here
let's see if that works out.
The stock is trading at $31
The put option is trading at $12.
On the left-hand side, right now,
it's trading at $43.
On the right-hand side, the call option
is trading at $8. And the bond is trading at $30.
So this combination is trading at $38.
So even though they have the exact same payoff
at option expiration, the call plus the bond
is cheaper than the stock plus the put.
So you have an aribtrage opportunity
an opportunity to make profit from a discrepancy
in price from two things that are essentially equal
and what you always want to do
is buy the cheaper thing and you want to sell
the more expensive thing. Especially when they
are the same thing, when they are going
to have the exact same payoff in the future.
So you want to sell this.
So, buying is pretty straightforward.
What does it mean to sell this over here?
Well, you could short the stock,
that's essentially you're selling the stock,
and then you would, essentially you are
shorting a put option. Another way to
think of it: you could write a put option.
So you would short the stock plus write a put.
So what would happen there?
Shorting the stock, you're borrowing the stock
and selling it. You're going to get $31
from shorting the stock.
And writing the put, literally means you are creating
a put option and selling it to someone else.
And so you're going to get $12 for that.
So you're going to get your $43.
And you're going to buy the call and the bond.
You're going to spend $8 on the call
and $30 on the bond, you're going to spend $38.
And you're going to make a profit of $5.
We're going to see in the next video: you make
this profit up front, and no matter what happens
to the stock price going forward,
you're able to arrange things so everything else
cancels out and you can just keep your $5.