Hey guys,
I was just reading this example of an arbitrage opportunity due to put call parity.
Basically, the expected value of the underlying asset is 20.
The futures bid is 18.5 and ask is 19.5
The call (with strike price 20) has a bid of 6 and an ask of 7.
The put (with strike price 20) has a bid of 1 and an ask of 2.
Basically, what the example says is to buy a put (for a price of 2) and sell a call (receiving 6) at strike price of 20. It also mentions to buy a future at 19.5. It goes on to mention that using the put call parity formula is not equal because 6-2>20-19.5, thus creating an arbitrage opportunity.
I don't have a problem understanding the formula and why there is an arbitrage opportunity, however I'm a little foggy on how this arbitrage would play out. These are the two examples that I can forsee taking place:
The price of underlying rises to 30, thus, the buyer of the call you sold will exercise it. Meaning you lose 10 dollars there. You will not exercise the put so you lose 2 dollars there. You receive 6 dollars as call premium. You also gain 10.5 dollars on the future that you bought, putting you at a net of 4.5 profit.
The price of the underlying drops to 12, thus, the buyer of the call will not exercise the option, gaining you 6 dollars through the call premium. You will exercise the put that you bought gaining you 8 dollars. You will lose 2 dollars on the put premium. On top of that, you will lose 7.5 dollars on the future that you bought. Thus, your net profit is 4.5 once again.
Have I got this right? Is your net profit in this arbitrage opportunity always going to be the profit you made from the premiums of the call and put PLUS the difference in the futures spot and expected value (thus, (6-2)+(20-19.5)=4.5)?
Thanks a lot for your help.
Ignoring interest rates (which usually for stuff like this you would) you can use Put/Call parity to to determine that at the offer price of the futures (19.5) the put should be worth .5 more than the call. The put has .5 of intrinsic value and the call has 0. They will have the same time value since they are the same strike (assuming the same expiry). Since you are collecting $4 when you should be paying $.5 you are correct that you will always net a $4.5 profit in the above scenario.
Buying a put and selling a call is the equivalent of selling a future. So you used options to sell a future and offset that with a long future. You synthetically sold the futures at 24 (your strikes were 20 + the 4 you collected) and bought it back at 19.5 on the offer. Again showing a net profit of $4.5. Any rally in the underlying will cost you money in the options but make you money in the futures at a 1:1 relationship and vice versa for the selloff.
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