What Is the Relationship between the Put-Call Parity and the Box Spread Strategy?

Put-call parity is a fundamental concept that states a synthetic long asset (long call and short put) must equal a long asset plus a financing component (a bond). A box spread is essentially a combination of two synthetic positions: a long synthetic forward and a short synthetic forward, but at different strikes.

When executed correctly, the box spread's fixed payoff is a direct result of the put-call parity holding true across the two strike prices. Any deviation is a potential arbitrage opportunity.