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## Finance and capital markets

### Course: Finance and capital markets > Unit 9

Lesson 1: Put and call options- American call options
- Basic shorting
- American put options
- Call option as leverage
- Put vs. short and leverage
- Call payoff diagram
- Put payoff diagram
- Put as insurance
- Put-call parity
- Long straddle
- Put writer payoff diagrams
- Call writer payoff diagram
- Arbitrage basics
- Put-call parity arbitrage I
- Put-call parity arbitrage II
- Put-call parity clarification
- Actual option quotes
- Option expiration and price

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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.

## Want to join the conversation?

- i think i'm dumb. i can't still understand why P+S should be equal to C+B. Any of you can elaborate more on that for me?(13 votes)
- You are not dumb. Please review the video several times starting with video 93, then continue with viewing several times each succeeding video. You'll get it!(14 votes)

- what's a point of this whole combination if you could just buy a @30 bond, sell it at 35

at expiration and make the same profit + save money on broker commission ?(8 votes)- In the video example it would coincidentally work out that way. However, let's assume that the stock has a price = $30, put-opt. w/ strike price = $40 currently selling @ $7, call-opt. w/strike price = $40 currently selling @ $19, both options have same expiration date, and a Rf Bond is worth $40 at same expiration. In this case, S + Ps = Cs + Bs → 30 + 19 = 7 + 39 → 49 = 46. In this case, your arbitrage profit is $3 whereas the Bond profit would be $1. $3 > $1(6 votes)

- Does this ONLY work with European options?(2 votes)
- Yes,early exercise is a risk with American options, especially around dividends.(1 vote)

- this is an oversimplification. bonds = usually have a probability of default associated with it (ignored by this equation) as well as transaction fees (this is more obvious). i wonder how you would incorporate the default probability into this. just a discount factor to the bond price?(2 votes)
- Present value of the bond has the probability of default built into it.(1 vote)

- I don't understand. If you were to buy a bond for $30 and recieve $35 from it. Why would you need to short the stock, buy a put and call too? Don't they all cancel out and you are left with a $5 profit. Would you not recieve the same $5 profit if you just bought the bond? Or am i missing something here? What outcomes happen from just purchasing the bond?(2 votes)
- Pawandeep, yet it says "Risk Free" in pink next to the Bond. So the bond gain of $5 is risk free. So we don't need the other S, P, C aspects. Surely we just buy the $30 bond for a "risk free" $5 at expiry. I am with sreten1 in not understanding the point of the bond component.(1 vote)

- So in the reverse situation, where bond and call are more, are you just supposed to short the bond?(2 votes)
- In the reverse situation you would short the bond and write a call. Then buy a stock and a put.(1 vote)

- What does he mean by Parity arbitrage?(1 vote)
- That the payoff of P+S is equal to C+B is called the put-call parity (video 93 on finance playlist). He's doing arbitrage (video 96 on finance playlist) by recognizing that P+S has a different prize than C+B. Together this becomes "put-call parity arbitrage".(2 votes)

- Why would a put option strike price be greater than the current trading price of the Stock?

In the example, the Stock is trading at $31/share, but the Put Option strike price is $35.

Doesn't that mean as soon as I buy that Put Option, the Put Option has $4 value.(1 vote)- Yes, so you will have to pay more than $4 for it.(2 votes)

- Why would a put have a strike price ($35 in video) higher then the market value of a stock price ($31 in video)? I thought you're betting that the market price of the stock is going to fall...so it doesn't make sense to me that the strike price of a put and call are the same...(1 vote)
- A put is the right (but not the obligation) to sell at a certain price. If you buy a put at $35 when the stock is at $30, we say that the put is already "in the money". But still if the stock goes down to $25, the put is even more in the money, so its value goes up by (roughly, not exactly) $5.

Normally the buyer of a put or call does not expect to actually sell the stock or buy the stock. The buyer plans to sell the put or call before the exercise date.(2 votes)

- can someone write a put option to a stock that he doesn't own?(1 vote)
- Sure. Why would you need to own the stock to write a put? Writing a put means you are selling an option to someone else to sell you their stock at the strike price.

Maybe you meant buying a put. You can of course buy any option you want to buy without having to own anything else.(2 votes)

## 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.