Put-call parity arbitrage II | Finance & Capital Markets | Khan Academy

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Put-Call Parity Arbitrage II. Created by Sal Khan.
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[@eminog01]

This is a pretty poor example because the p and c are equal at S=35. There is no real arbitrage going on in this example, only the appreciation in value for the bond. The arbitrage makes $0 but the appreciation in the bond makes the $5. Arbitrage could arise if the put was valued at 100, in which case selling it took in $131. Buying the call and bond costs $38 but appreciates in value to $43. The net result is a profit of 131-43=$88 from arbitrage, and $5 from the bond, so $93.

[@mr_monaco]

when you factor in commissions, arbitrage opportunities are even more rare

[@mattmarkham4734]

I'm confused. Why would you not say that you would make -$8 from call, $31 from short sale, -$23 from put, $5 from bond for a grand total of $5 in the end???

[@Alan-bx9qp]

Can you look at it another way? when stock price rises to $70, you exercise your call option. You simply to need to raise $35 to buy stock. Then with this stock, you can already returned it to whoever you borrowed from. The money raised to buy the stock can come from the bond you are holding. so is basically 35 - 35 = 0. why is it 35+35-70=0

[@wujiali144]

I agree. With a call option in hand, can just buy the $70 stock at $35.

[@mark653]

this is a great way to think about it!

[@elroyblackbean]

LOL. "Spend time learning this great concept...which almost never happens."

[@debayansen3705]

In the 2nd senario , I have a dissatisfaction with your explanation . What if the stock price goes up to 71 instead of 70 at expiration ? 35 from bond p+ 35 from call won't make it 71 . So obviously , the explanation should've been , " we already bought the stock worth 70 at 35 due to the call option and we will use this stock to cover the short sell"

[@ZainShamim]

if stock price goes up to 71, you're call is worth 36 now

[@varunahuja2080]

A small mistake in the 2nd explanation. Please correct me if I'm wrong. In the 2nd explanation, the price of the stock is 70, right, but we have the call option, using which, we can buy the stock for 35 And the amount 35 is obtained from selling the bond whose final price is 35. Right?

[@rajshah8143]

You could also take a generic example setting the stock price as x. Then make two cases: (i)x35 Net always comes out to be zero.

[@Ferrus91]

Does the value of the bond at expiration have to be equal to the strike prices of the options?

[@eminog01]

They do have the same price, but the video implies that the arbitrage is the source of the 5 dollar profit and that the user should be doing this arbitrage in this situation because it makes the user 5 dollar profit. That is not correct. Instead, the profit is from the appreciation of the bond. The user could have done no arbitrage and still made the profit.

[@rsdighe04]

I am always wondering why not just exercise the call option at 35 (scenario 2) to cover for our short. With that said would we not have a gain of 40?

[@ashishashuyou]

How do u get that $35 to buy stock from call seller?? By selling bond worth $35. So ending up with $5 only

[@phongvo9989]

i got confused. we borrow and sell stock at 31, in case of stock went down in the future, we would have $35 bonds to offset stock at $35 from put holders, so we would have stock. but we borrowed stock at $31 and now we give stock back, for example, current price at $20, we have made 31-20=$11 additional profit from shorting stock, so the total profit not only $5, but $16 right?

[@phongvo9989]

and in case of stock went up to $70, you would have bond worth for $35 and call to buy stock at $35, so no matter how the stock price went up, we still could offset the stock borrowing by call option. Therefore, we not only make $5 arbitrage profit, but $35 bonds as well at expiration. Am i right? if not please help me correct it, thank you :)

[@Alan-bx9qp]

What if price became $20. The other party will exercise the put option. So, in this case, i will definitely be forced to buy his/her stock at $35. the money can come from the bond worth $35.

[@crfletcher11]

Excellent explanation. Clear and concise. Thank you!

[@omi4763]

If you have a call option with strike price of 35$, why are you not exercising it to buy shares of current price 70$? Why are you using bond money to cover the short?

[@GSD-]

What about margin calls?

[@MultiCheeseGrater]

WTF I'm confused make the videos longer plox like the other finance videos that's how I like em

[@jk12324]

But a main assumption underlying the put-call parity is that they both have the same strike price, which in this example is $35. Put-call parity wouldn't hold if they were different.

[@AJG6150]

This is all nice, but if we have to wait until expiration for "everything to cancel out," why not just buy the bond outright in the first place, and collect the $5 of interest at expiration?

[@bxmbino]

+ArashkG The arbitrage opportunity means you can profit without any initial investment, the initial cashflows are positive and the cash flows at maturity are neutral.

[@AJG6150]

Thanks for the explanation. However, in a practical sense, I think this still remains rather silly. Although you buy and sell "immediately," you still need the capitol in the first place so you can buy. All this really does I guess, is free up the capitol rather quickly so that you can use it for something else (maybe more of the same thing).

[@bxmbino]

Not quite, if you sell first then you can generate returns without any initial capital

[@AJG6150]

I stand corrected. You've got me cornered haha

[@bxmbino]

+ArashkG haha!

[@robertsandoval9113]

what bond is that?

[@l.p.2500]

Anyone knows how to do this one? Consider a put option on Stock A with maturity 2 years and strike 13 EUR. The put option premium is 3.6045 EUR, and the stock's spot price is 10 EUR. If the risk free rate is 4.50%, What is the premium of a call option with the same strike price and maturity as the put option?

[@taecod]

K= 13 P=3.6045 S=10 r=4.5% P+S-C=PV(K); 3.6045+10-C=13/(1+4.5%)^2; C=1.7

[@l.p.2500]

ty dude

[@falleruen]

This only works for European put and call options. If you issue an american put option, an individual could exercise their put before the bond matures.

[@poiuwnwang7109]

He clarifies it in the next video.

[@rogjerr]

What about commissions and taxes?? I don't think you walk away with $5.

[@hengbinzhang3155]

how does the put & call option be valued at $12& $8? if current stock price is $31 and option strike is $35, shouldn't them be $4 and $0 ?

[@Furthere]

Hengbin Zhang Hey, The put and call options are valued as compensation for the put issuer's risk. See it as a premium that you have to pay. So the issuer chooses an appropriate price (rate) to value the options at. Depending on discount rates (not given) etc, accounts for the price of the option

[@phongvo9989]

@falleruen you are right :)

[@MyLegsAreKindaLong]

I am very confused

[@stevenz995]

how about just buy the 30 bond and sell it 35....

[@sunnylu216]

you need $30 to buy the bond. With the arbitrage you don't need anything other than trading fees. Its kind of like if your friend is selling a car for 3000. And you happen to know someone looking to buy the exact same car for 3500. So you ask to borrow it for a bit and end up selling it for 3500, and giving 3000 to your friend. You didn't need to have any money to begin with.

[@cade7458]

@@sunnylu216 why couldn’t they have just said this😂

[@GreifNation]

He did his math wrong... the put price would be $3500 as the put would require him to buy 100 shares at $35

[@shauthentic]

Eminog016 is correct, and the video is wrong. This video mistakes the bond appreciation to arbitrage. The 2 options ARE IN parity and NOT out of parity. he said.... eminog016 months ago They do have the same price, but the video implies that the arbitrage is the source of the 5 dollar profit and that the user should be doing this arbitrage in this situation because it makes the user 5 dollar profit. That is not correct. Instead, the profit is from the appreciation of the bond. The user could have done no arbitrage and still made the profit.

[@btc1m654]

Sure. Though in the case of the video you wouldn’t need an upfront investment

[@ilyak.6953]

Easy money (c)

[@cincinati6391]

@Pharaohilife Arbitrage means you exploit the conditions and make profit. In the present video you have zero investment and you are ended up with profit of $5. By employing this parity you are able to buy the bond with zero money.

[@jjkul1]

first view and comment :P...