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Put-call parity

The concept of put-call parity is that puts and calls are complementary in pricing, and if they are not, opportunities for arbitrage exist. Explore the concepts of put-call parity in this video. Created by Sal Khan.

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  • blobby green style avatar for user patton.dan
    The P/L payoff diagram for the Stock + Put seems identical to the payoff diagram for just the Call on its own (i.e. with no Bond) in the previous video. In both cases it is flat at -$10 while the stock price is <$50, $0 when the stock price hits $60 and +ve for all stock prices >$60. Where does the Bond fit in?
    (12 votes)
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    • orange juice squid orange style avatar for user FishHead
      The bond doesn't affect the P/L, it simply affects the value.

      If you buy a call without a bond, it's worth $0 at/below $50 (value). You lose $10 (P/L). With the bond, the combination is worth $50 (from the bond) at/below $50 (value). You still lose $10 from the call (P/L). The bond is ALWAYS going to pay $50, unlike the call which fluctuates in value with the stock price, so it doesn't figure into a graph of profit/loss. It's a constant.
      (3 votes)
  • blobby green style avatar for user Ben Gomez
    I am still confused about the bond. Would you make a video to explain the purpose of the bond? Maybe it's advantages and definition?
    (8 votes)
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    • blobby green style avatar for user Rick Youngfelt
      I think the "bond" acts as an "asset floor" for the buyer of the call. However, I have never seen put/call parity explained in this manner. I found it a bit confusing as well. I think that put/call parity becomes much easier to understand when one is instructed on riskless arbitrage of options using conversions/risk reversals (e.g. netting profits on Buy Call, Sell Put, Sell Stock).
      (2 votes)
  • male robot johnny style avatar for user Fardin Humayun
    From my understanding, if we hold a bond, its price may change depending on the prevailing interest rate in the market. So, technically we would not be holding a $50 bond at all time right? If my argument is correct, wouldn't it be better if we simply hold cash of $50?
    (2 votes)
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    • ohnoes default style avatar for user Tejas
      The price of the bond itself may change over the period, but the value of the bond at maturity is guaranteed to be $50. Before maturity, the bond price will be the present value of the maturity value, which does depend on interest, but at maturity, the bond price does not depend on interest rates.
      (6 votes)
  • female robot amelia style avatar for user Vg
    What about buying a call option as insurance when intending to short a stock? Is this done? Is there a downside? For example:
    - You borrow a stock (that is worth $50) and sell it at $50 with the intention to short once the stock price drops to $20
    - You buy a call option with a strike price of $50
    - Instead of going down, the price of the stock rises. But you don't lose money (except for the call option price) because you can still exercise the option to buy the stock back at $50.
    (3 votes)
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  • leaf green style avatar for user CPORIII
    Put call parity is a term to describe a call and a put of the same strike and the price of the underlying stock. It is a three way relationship in that there is an equilibrium in the prices of each. And if the prices are not valued accordingly than an arbitrage opportunity occurs and a profit can be locked in synthetically. If a put is offered below fair value relative to the three way relationship then you purchase the put and synthetically sell the same put by buying the stock and selling the call in the same strike. So I'm not sure why the use of a bond in this example of put call parity.
    (4 votes)
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    • male robot hal style avatar for user Andrew M
      You are mistaken about what the term means.
      Put call parity refers to what sal talks about in this video. You can create a put with a call and a bond and a share of stock, and you can create a call with a put and a bond and a share of stock, and since the bond and the share are the same in either case, there must be a definite relationship between the price of a put and the price of a call.
      (0 votes)
  • piceratops ultimate style avatar for user Mike Xie
    can put and calls be used on bonds as well, not just stock?
    (2 votes)
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  • blobby green style avatar for user RAMESH ARAVIND
    Here put call parity is used to reduce the investment risk for the investor . Is it right?
    (1 vote)
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    • male robot hal style avatar for user Andrew M
      No. Put call parity is really just an academic way to show how and why put and call prices have to be consistent with one another. If they aren't, then there would be an arbitrage opportunity (risk free way to make profit), and arbitrage opportunities are not supposed to exist for long (in most situations)
      (2 votes)
  • old spice man green style avatar for user chrisbodikian
    This might be a stupid question, but wouldn't the bond price also go up or down? Surely it wouldn't always be stable. Maybe I'm missing some basic data.
    (1 vote)
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  • leaf blue style avatar for user Fedro Christian M
    Hi there, I'm still a litle bit confused about the bond + call options. Will it gives the same result by shorting the stock and buy the call option? Thank you.
    (1 vote)
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  • blobby green style avatar for user Artour Khouzin
    shouldn't the bond be discounted? because the put call parity formula is S+P = C+K/(1+r)
    k being the strike price (bond) in this example
    (1 vote)
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Video transcript

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 costs to enter the position on this one on the right. Now the question I want to answer in this video is 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 to 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 at 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. If the stock price goes to $60, you would exercise your option to buy at $50, and then you could sell at $60 and you would make $10. So 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 essentially shift this entire graph up by $50. So we could have, essentially, a $50 bond, or a bond to that is worth-- let me write it this way. A bond that is worth $50 at option expiration. So if there's some interest we're getting, we 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 you have the value of the bond plus the call option. So at $60, the call option's worth $10, the bonds worth $50, the combination is worth $60. And so the combination of the call option plus the bond, you'll see it here on the left, it's actually going to have the same payoff diagram as the stock plus the put. So you have the situation here that a stock plus an appropriately priced put or a put with a appropriate strike price is going to be the same thing when it comes to payoff, 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.