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Put-call parity arbitrage II

Put-Call Parity Arbitrage II. Created by Sal Khan.

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  • blobby green style avatar for user Rick.Thompson
    If you purchase the bond at 30 and sell it for 35, you make 5 (theoretically risk free).
    the short, the put and the call all seem to cancel each other out. In the end, you wind up with $5. So what is the point of arbitrage when the bond yield the guaranteed $5 in the first place.

    Does the have any practical application regarding puts and calls?
    (19 votes)
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  • blobby green style avatar for user Jouni Mikael Mäkelä
    How do you write options?? I mean, how does it work in reality. Can i just go to my brokerage and say that I want to write a put-option for a certain stock?? Can I do this online also (for example in some options trading website)?? If so, how can I do it there?
    (8 votes)
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    • blobby green style avatar for user mullachv
      If you have an options trading account with a brokerage firm, you'll see that there are standard options contracts for most stocks. And they are tabulated with Write pay-offs and Buy prices. For e.g. for stock ABC, they will have option table similar to something like below - by the way, there are naming conventions on how options are named and their expiration dates (2nd Friday - I think of the month):
      ABCAA (call option strike price $35 on Dec 15, 2011): $5
      ABCAB (call option strike price $35 on Jan 17, 2012): $7

      ABCDA (put option strike price $33 on Dec 15, 2011): $4
      ABCDB (put option strike price $30 on Jan 17, 2012): $1

      etc. etc.

      Now, you can only buy or sell any of these pre-defined options. When you buy, you are the purchaser of that option. When you sell, you become the option writer.

      You can do this online at many brokerage firms - Etrade, scott trade etc. etc.
      Does that help?
      (20 votes)
  • blobby green style avatar for user rojahon
    In the case where the stock goes to $70, why can't you use the call option to cover your short? That way, covering the short only costs you $35, rather than $70, and you get to keep the $5 plus the $35 from the bond.
    (6 votes)
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    • blobby green style avatar for user not_ben
      You do use the call to cover your short - at last partially. Think of it this way - you have to come up with a $70 share that you don't have. Your call entitles you to buy that share for $35 - but you still have to come up with that $35. That $35 comes from the bond.
      (5 votes)
  • blobby green style avatar for user Bob Marlin
    At , wouldn't you also get the profit from writing the put? So, you're profit would be the risk-free $5 you make plus the $12 from writing the put?
    (5 votes)
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  • blobby green style avatar for user phani.mogalapu
    Can we say that this video is a round about way of saying that if the call option < put option (or vice versa) for a given stock price we can make risk free money?
    (1 vote)
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    • blobby green style avatar for user Marshall Stanton
      Another way to use this formula is say that you know three of the factors - stock, call, and put - but that you don't know the value of the forth (in this case, the bond). You can then use basic arithmetic to figure out what the price of a bond would have to be for you to break even and then check this value against other bonds that are being traded in the market to see which side is more likely to be higher.

      For instance, say we have a stock at $35, a put trading at $10, a call trading at $12, and both options have a strike price of $40. S = 35, P = 10, C = 12. In that case, 35 + 10 = 12 + B. B = 33. So we know we'd need to find a bond trading at $33 whose strike price is $40 in order to break even. That's 21% interest, so any bond with 21% interest should yield us the same result. But say 21% interest is very hard to find, so we might just assume that the Stock-Put side is going to be worth more and so we'd short stocks and write puts, but buy calls and bonds for whatever we can get and make our money that way.
      (6 votes)
  • blobby green style avatar for user Yair Sánchez
    so in reality we would not see this opportunities happening?
    (3 votes)
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  • blobby green style avatar for user S R
    Suppose the stock price decreases to 1 or 2,in that case
    0 : you still wont exercise the call option
    -2 : buy stock to cover short
    -35 : buy stock from put holder
    +35 : get from bond
    So here you are losing $2 so net you profit <$5. Please clarify
    (2 votes)
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    • blobby green style avatar for user sammcardle30
      If the stock price decreases to $2:
      The call option is not exercised: +$0
      The bond is sold: +$35
      The stock must be bought from put holder: -$35
      The stock can then be sold in the market: +$2
      The stock must be bought to cover short: $-2
      Here the total sums to $0, so you still make $5 profit (above, you forgot that you can sell the share in the market once you have bought it from the put holder)
      (3 votes)
  • blobby green style avatar for user kev.rampal
    what if the stock price is worth $75? To cover the short you will have to pay $75 which cannot be financed by the bond worth $35 and the call of $35
    (1 vote)
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  • blobby green style avatar for user Toad62
    Does this example require the use of a european option where the option must be exercised on a specific date? Otherwise there is a chance that the put owner could exercise prior to the bond maturity date.
    (1 vote)
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    • male robot hal style avatar for user Andrew M
      Options are never exercised prior to the expiration date because that just wastes the option value. If you have an option that is in the money and you want the cash before the expiration, you just sell the option, you don't exercise it.
      (2 votes)
  • duskpin seed style avatar for user davinci.rishi
    I believe an important point not given enough importance in the video is the price of the bond at the option expiration. If the price of the bond at option expiration is NOT equal to the strike price of the put and call options, the put call parity principle wouldn't hold true is it?
    (1 vote)
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    • male robot hal style avatar for user Andrew M
      The bond has to be worth face value at the time of expiration. The bond in put-call parity calculations is assumed to be a zero coupon that matures at the expiration. The point is just that the interest rate that is built into the bond is also built into the pricing of the options.
      (1 vote)

Video transcript

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.