Put as Insurance and Put-Call Parity
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Put as Insurance and Put-Call Parity

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If we want to get the upside of owning a stock
while still mitigating the downside in case the stock price goes down
We saw that we could buy a stock and an appropriate put option
so that when the stock goes below some price
the put option starts to have value and so it mitigates our downside
And just as a review, these payoff diagrams are the values of, or at least the one on the left,
is the value of holdings at some future date
and we are defining that date to be the maturity date of the options under question
Now, and this one over here is the profit at that maturity date
and that's why we are subtracting the actual costs to enter the position on this one on the right
Now the question I want to answer in this video is, "How can we get the same payoff diagram without buying either stocks or puts?"
and as a bit of a clue, think about what happens if we were to just buy a call option
actually let me do it in that same color
So if you were to just have a call option, the payoff diagram would look like this.
You would never exercise the call option at expiration
unless, and we're assuming this is at expiration or at maturity,
but if the stock price goes above $50, you would then exercise your option to buy it at $50
So then it starts to have value as the stock price goes above $50
If the stock price goes to $60, you would exercise your option to buy at $50 and then you could sell at $60
and you would make $10
So you start to get some of the upside
So how can we shift this graph up to get exactly the same payoff diagram?
Well, we could have a call option and we could own something that would essentially shift this entire graph up by $50
So we could have, essentially, a $50 bond, or a bond that is worth, let me write it this way, a bond that is worth $50 at option expiration
So if there's some interest we're getting, we might be able to buy it for a little bit less
If there's zero interest, then it's pretty much like cash and we would pay $50 for it
But the payoff diagram for a bond that will be worth $50 at this date, at maturity, or at expiration
The payoff diagram for just the bond would look like this. It would just a straight line.
It's guaranteed to pay you $50
So if you own the bond and the call option, below $50 the call option is worthless, so you're just going to have the bond over here
And then, above $50, you still have the bond, but now the call option is worth something
So you have the value of the bond plus the call option
So at $60, the call option is worth $10. The bond is worth $50. The combination is worth $60
And so the combination of the call option plus the bond, you see it here on the left,
it's actually going to have the same payoff diagram as the stock plus the put
So you have the situation here that the stock plus an appropriately priced put
or a put with the appropriate strike price is going to be the same thing
when it comes to payoff at a future date, at expiration, as a bond plus a call option
And this right here is called "Put-Call Parity"
and it shows the relationship between all of these different securities
and if any of these prices start to, kind of, not make this thing hold true, there might be an arbitrage opportunity, but we'll cover that in future videos.


let's say that company abcd is some type of pharmaceutical company
that has a drug trial coming out
and you're convinced that
it's trading at 50 dollars a share
but you're convinced that if the drug gets approved
that the company's stock is going to skyrocket
and you're also convinced that the company
if the drug gets rejected that the stock price
is going to tank to maybe 5 or 10 dollars
so if you want to make money
off of that beleif
and I'm not necessarily reccommending
that you do it
it's always tricker in reality than it sounds on paper
but one way that you could would be to buy the call option and the put option
on that stock
the put option is going to make you money if
the stock tanks
and then the call option is going to make money
if the stock becomes, if the drug gets
approved and the stock skyrockets
so let's actually draw the payoff diagram
so if the stock goes down
if the stock goes down
let's say it goes down to zero
you sould exercise the put option
you could buy the stock for 0,
excercise the put option
and sell it for 50 dollars
this is the right to sell the stock for 50 dollars
and of course we're talking about the value of the combination at expiration
so if the stock is worth zero at experation
then the put is worth 50
the call option is clearly worthless
you wouldn't exercise the call option if the stock is worth zero
you wouldn't want to buy something for 50 dollars that's worth zero
so from the stock being worth zero
all the way up to the stock being worth 50
you would want to exercise the put option
but the value of the put option is going to become lower and lower and lower
and anything above 50 you wouldn't exercise the put option at all
if you get above 50, you would want to exercise your call option
if the stock is worth 60 dollars at expiration, then your call option is worth 10 dollars
because you have the right to buy something at 50
which you can sell for 60
so then you have the value of your call option
going up
so you can see a situation here when you think about the value
of this bundle of the call plus the put option
that it's not much value if the value of the stock doesn't change
from 50, your options are worthless
but you have a major movement
either to the upside or the downside,
then this straddle it's called
when you buy, when you go
long a call and long a put
this is called a long straddle
you benefit from a major price movement
when you think about it from the profit or loss point of view
you just shift it down from the
amount that you paid for the two options
in this case we paid 20 dollars for both options
so in this case where we exercise the put
instead of making 50 dollars
we have to net it for the 20 dollars we paid for the options
so we would only make 30 dollars
and at the point where we're not exercising either option
because they're both essentially worthless
there's no reason to exercise them
then essentially we have just lost 20 dollars
for both options so we will be down over here
and then anything above 50 dollars will start to make money
so let me draw the option diagram over here
it will look like this
the payoff diagram
it will look just like this
so when you actually factor in how much you paid for the options
you now see that you only would make money with this straddle
if the underlying stock price
myabe after the results of the trial
hopefully they get released before the maturity of the options
if the stock goes in this area
if the stock goes below 30
or if the stock goes above 70
but if it has one of those major movements,
then this position, this straddle
this long straddle will make you money

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