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Market Outcomes

Look at different market outcomes demonstrating that this position allows individuals to profit by arbitrage regardless of where the underlying market finishes.

The futures price finished below 105 at expiration. Our short 105 put is now in-the-money and will be exercised, which means we are obligated to buy a futures contract at 105 from the put owner.
When this trade was executed, we shorted a futures contract at 100, therefore our futures loss is $5, given the fact that we bought at 105 and sold at 100. This loss is mitigated by the $8 we received upon the sale of the put. The put owner forfeited the $8 when he exercised his option.

Our long 105 call expires worthless, so we forfeit the $2 call premium. This brings our net profit to $1 with the loss of $5 from the futures and loss of $2 from the call and the gain of $8 from the put.
Another scenario, the futures price finished above 105 at expiration. Our long 105 call is now in-the-money allowing us to exercise the call and buy a futures contract at 105. Because we exercised the option, our $2 premium is forfeited.

When this trade was executed, we shorted a future at 100, therefore our futures loss is $5. The $8 we received from the sale of the put is now profit because it expired worthless. If you add up the $8 gain from the put, less the $5 loss from the futures and $2 loss from the call you would net a profit of $1.

If the futures end exactly at 105, both options expire worthless. We lose $5 on the futures and make net $6 in options premium, therefore, we net $1.

We stated earlier that put-call parity would require the put to be priced at 7. We have now seen that a put price of 8 created an arbitrage opportunity that generated a profit of $1 regardless of the market outcome.

Put-call parity keeps the prices of calls, puts and futures consistent with one another. Thus, improving market efficiency for trading participants.

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