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Today we will learn about put call parity and how it works,

Hello you two so welcome back to my channel today we’re going to talk a little bit about put-call parity so we’ve just done a couple of videos one on covered calls and one on protective puts and we pointed out that when you trade one option and you trade the underlying alongside it either long or short you end up with a payoff that is the same as another option

And we think that’s kind of an interesting thing and the big question then is is there a formula that that ties these things together and of course there is and that formula is put-call parity so the put-call parity formula ties together options calls inputs as long as they have the same underlying the same strike price and the same expiration so we can’t tie

Together other types of options also it requires that they be european options not american options so from the very beginning in fact when when options were first listed there were actually just call options listed rather than calls and puts and this is because it was well known the concept of put-call parity and therefore you could get the payoff of a put

Or the payoff of a call by just trading a call option so if you wanted the payoff of a put you just had to combine a position in the underlying with that call option so up here on screen right now is our formula for put call option and the the formula is put plus 5 equals call plus the present value of the strike that’s what our last bit k to the your t it’s

Just present value of the strike so when we combine our options with the underlying we get the payoff of a different option and it must follow this this formula and the reason it has to feel like it’s not just a theoretical thing that doesn’t have to happen it actually does have to happen because if there were two portfolios that had the exact same payoff and

So no matter what happened in the market if you ended up at expiration with the exact same amount of money it would be an arbitrage opportunity if if they didn’t trade at the same price today and so there’s lots of traders out there that will be looking for for puts and calls that or miss price relative to each other and trading them against each other and for

That reason you know the buying and selling pressure mean that these things do they have to and they do stay in line with each other so yes so our formula is as i said put plus 4 equals call plus present value of the strike and obviously then we can just play around with that formula we’re able to i if we know some of the details but not all of them so if we

Know the prices of the puts and calls the strike price in the expiration where a and of course the interest rate we are able to back out the price of the underlying or if we know the price of one of the options we can back out the price of the other option and so on or even the interest rate so that is to put called parity formula with a little algebra we can

Turn it into an array of different formulas that give us the same information and and that’s really it you know that’s put-call parity so let’s just walk through a quick example of that so we’ll say if we have an underlying that’s trading at 31 and then there’s put and call options available with a strike of 30 so both the put option is a strike of 30 and the

Call does our interest rate is 10% and there is a three-month call option available it’s trading at $3 the put option is trading at 2.25 and we just ask ourselves is there an arbitrage opportunity so in order to answer that question all we have to do is pump all of our numbers into the formula so we basically look at each side of the equal sign and call that

A different portfolio and they they just have to be equal to each other so portfolio b we’re calling p + s0 so to put plus the spark price so that’s 225 plus 31 and that gives us thirty three dollars and twenty five cents and then portfolio a is the call option plus the present value of the strike so the the call option is trading at three dollars the strike

Is 30 so we present value that add them together and we come to thirty two dot twenty six cents so as you can see thirty three dollars and twenty five is not the same as thirty two dollars and twenty six so there is an arbitrage opportunity so in order to take advantage of that arbitrage you just buy the cheap one and sell the expensive one so we’re gonna sell

Portfolio b by portfolio a and we would make an arbitrage profit of 99 cents hopefully you found that useful if you’re interested in studying along with the book i’m using trading pricing financial derivatives which is a book that my partner and i rode and all of these examples are worked out in the book and you know have a great day and i’ll see you tomorrow

The next videos up are going to be on combination so we’ll be looking at straddle strangles spreads and butterfly spreads all those sorts of things so if you if you want to see more videos like this don’t forget to hit the subscribe button and and if you like this video if you found it useful hit the like button have a great day bye

Transcribed from video

What is Put Call Parity? How does it work? By Patrick Boyle