Buying a call and selling a put with the same strike price creates a way of buying the underlying asset at the strike price. This gives a profit and loss close to that of buying futures. Conversely, buying the put and selling the call gives a profit and loss close to that of selling futures1. This combination is called a synthetic forward and is treated as equivalent to buying a forward contract2.
Consider a hypothetical example in which you buy a call with a strike price of 100 yen for 6 yen and sell a put with the same strike price for 4 yen. You pay a net 2 yen. If the price of the underlying asset at expiry is 110 yen, you receive 10 yen from the call and the put is not exercised, so the profit is 10 − 2 = 8 yen. At 90 yen, the call is abandoned and you pay 10 yen on the sold put, so the loss is −10 − 2 = −12 yen. In both cases the payoff at expiry is "price of the underlying asset − 100 − 2", the same as buying the underlying asset at 100 yen plus a cost of 2 yen. The payoff matches that of buying futures only during the life of the option3.
If the strike price is set equal to the forward price of the underlying asset, the present value of this combination is zero2. This relationship follows from put-call parity.
Notes
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Osaka Exchange, "デビットスプレッド戦略" (Debit spread strategy) (in Japanese), which explains the synthetic relationship that buying a put and selling a call equals selling futures, and buying a call and selling a put equals buying futures (put-call parity). ↩
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The University of Texas at Austin, "9. Parity and Other Option Relationships", the section on "Synthetic" Forwards. It explains that buying a call and selling a put creates a synthetic long forward, and that the price is zero when the strike equals the forward price. ↩ ↩2
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The Options Industry Council, "Synthetic Long Stock", which explains that a long call combined with a short put has the same risk and reward as holding the underlying, only for the term of the option. ↩