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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?
• 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!
• 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 ?
• 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
• 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?
• 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?
• 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?
• In the reverse situation you would short the bond and write a call. Then buy a stock and a put.
(1 vote)
• 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.
• 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.
• 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.