Option strategy equivalent to Futures/Fwd


Could someone explain to me the following:

Buy ATM calls + Sell ATM puts is equivalent to Buy Futures/Fwd

Sell ATM calls + Buy ATM Puts is equivalent to Sell Futures/Fwd

I’m assuming that, since they’re both ATM, they should have the same price all things equal, thus the cost of buying a call = the premium received from selling a put. In futures/forwards, you do not have an upfront cost, which until now is replicating perfectly the instrument. At expiration, You will participate in the gain (through your call) or be obliged to participate in the loss (through the put) if the underlying goes down in value. Thus it is the same thing.

Vice versa for the second replication.

Thanks for your reply.

Understood the zero cost premium part.

But i don’t get how the option payoff replicates the futures/fwd

for eg. Like u said “At expiration, You will participate in the gain (through your call)” so there’s unlimited upside potential to a long call… but for futures isn’t the upside or downside capped?

The downside is capped: the stock value at expiration cannot drop below zero.

The upside is, for all intents and purposes, uncapped: the stock value at expiration can rise without bound.