Put-call parity

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 our holdings at some future date and we're 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're subtracting the actual cost to enter the position on this one on the right now the question I want to answer in this video is how can we 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 that 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 so the stock price goes to 60 you would exercise your option to buy it 50 and then you could sell it 60 and you would make $10 so your thought your 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 have 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 bond that is worth $50 $50 at option expiration so if there's some interest we're getting we could might be able to buy it for a little bit less if there's zero interest then it's pretty much like cash 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 be 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 if the value of the bond plus the call option so it's $60 the call options were 10 the bonds 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 of as the stock plus the put so you have the situation here that the stock plus an appropriately priced put or put with the appropriate strike price is going to be the same thing when it comes to payoff at 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 the 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