Put-call parity arbitrage II

Voiceover: So, I claimed in the last video that we made a $5 risk-free profit by spending $38 to buy a call and a bond and we got $43 by shorting a stock and essentially writing a put option. What I want to do in this video is verify that we really do have all of our basis covered. So let's just think about all of the different scenarios for the underlying stock price at option expiration because that's the date that we care about. So let's take this situation where the stock just becomes where the stock just goes to 0. In that situation the call that we own is worthless. The call is worthless. No reason why you'd want to exercise the option to buy it for $35 when the stock is worth 0. But the good thing is, is that when we now have to cover our short. Remember, when you short something you're borrowing the stock and selling it and in the future you have to buy the stock to cover your short. To buy the stock and return it to whomever you borrowed it from. So now, we can spend $0. We can now spend $0, $0 to buy stock and essentially give it back to whom we borrowed it from or should cover the short. To buy stock to cover or unwind short. To cover the short. The bad thing is, is that put option that we wrote. Remember, we wrote it. We sold the put option. We're giving someone else the right to sell to sell the stock to us for $35 and if the stock price is worth $0 they're going to exercise that option. Because they can then, they can buy the stock for 0 and they can sell it to us for $35. So, we have to spend, we have to spend $35 to buy ... to kind of buy the stock from put holder. From put holder. But the good thing is, is that we have this bond, we own this bond that's now worth $35. We have a $35 bond, 35. We have a $35 bond. So we can use the $35 bond to spend the $35 such to give the $35 to the holder of the put and everything cancels out. We can still keep our original $5. So, that's the situation where the stock price went to 0. What about the situation where the stock price goes to something crazy? Let's say the stock price goes to 70. So, the stock price goes up. We draw a column over here. So, now let's think about the scenario where the stock price goes to 70. Now all of a sudden the call option we have, remember it's an option to buy the stock at $35. The call, the call is worth, is worth $35. The call is worth $35. We have a bond that's going to be worth $35. A bond worth 35. The put option is worthless so the person who we wrote the put for they won't exercise it. So, the put is worthless. The put is worthless but we still have to cover our short. We have to buy back the stock and return the stock to whomever we borrowed it from and now to cover our short, to buy the stock is going to cost us $70. So, we're going to have to use this $70, the $35 from the call and $35 from the bond to actually cover our short positions. So $70 to buy stock and cover short. What you'll see is I just picked kind of a low, a low stock price and a high stock price but no matter what the stock price is you're going to be able to cover all of your obligations and break even at expiration and keep your original risk-free $5. Now the reality of the situation is that opportunities like this seldom exist because frankly people can write computer programs to find these arbitrage opportunities and just exploit them really, really, really fast.