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Put-call parity arbitrage I

When there is not put-call parity, there is an arbitrage opportunity. In the second of two videos on arbitrage and put-call parity, we explore how this works. Created by Sal Khan.

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Video transcript

Say stock XYZ is trading at $31. We have a call option on stock XYZ with the $35 strike price. It's trading at $8. We have a put option on stock 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 then finally, there's a bond. And this bond is unrelated to stock XYZ. It's going to be a risk free bond. So it could be some type of a treasury bill. Worth $35 at option expiration. And you can buy it right now for $30. And the reason why you can buy it for less is you pay $30, 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? And 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, and the put is a put on that stock, is equal to. It's going to have the same value at expiration as a call with the same strike price. A call 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. So 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. So that's plus 12. So this on the left hand side right now if you had to buy it, it's trading at $43. Is On the right hand side, you have the call option is trading $8. And then 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 arbitrage opportunity. You have 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 you always want to buy the cheaper thing. And you want to sell the more expensive thing, especially when they are the same thing, when they're 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 you essentially are shorting a put option. Or another way to think of it, you could write a put option. So you short the stock plus write a put. And so what would happened there? Shorting the stock, you're borrowing the stock and you are selling it. So you're going to get $31 from shorting the stock. And writing the put means you literally are essentially 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 then you're going to buy the call and the bond. So you're going to spend $8 on the call, $30 on the bonds. So you are going to spend $38. And you're going to make a profit of $5. And what we're going to see in the next video is you make this profit upfront. And no matter what happens to the stock price going forward, you're able to rearrange things so that everything else just cancels out. And you can just keep your $5.