A Long Call and Short Put Form a Synthetic Long Future

Summary

The document addresses how an at-the-money call and a short at-the-money put with the same underlying and expiry relate to a futures position. Its answer states that one call paired with one put creates one synthetic long futures position. This establishes the option contract pairing conceptually, rather than deriving the payoff or calculating a hedge ratio against a separately specified futures contract.

The explanation is brief and offers no numerical example, adjustment for contract multipliers, or discussion of dividends, rates, margin, or differences between forward and futures pricing. It answers the basic replication question at the position level; practical hedging still requires matching contract specifications and considering market conditions.

Key ideas

• A long at-the-money call combined with a short at-the-money put forms a synthetic long futures exposure.
• The answer treats one call and one put as one synthetic position.
• The document does not derive pricing adjustments or detail contract multiplier and expiry considerations.

Tags

# How to calculate equivalent futures position?


# How to calculate equivalent futures position?












Let's say I have the following two positions:

- Buy ATM SPX call, expires in 1 month

- Sell ATM SPX put, expires in 1 month

This creates a synthetic futures position. How do I calculate how many futures are required to replicate (or hedge) my options position?

## Answer by vonjd (score 3, accepted)

https://quant.stackexchange.com/a/1476

Perhaps I don't understand your question correctly but

one Synthetic Long Futures Construction equals "Buy one ATM Call" and "Sell one ATM Put"

(see e.g. here: http://www.theoptionsguide.com/synthetic-long-futures.aspx)

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.