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Can a Synthetic Long Position in the Underlying Asset Be Created Using American Options?

A synthetic long position in the underlying asset (e.g. Bitcoin) can be approximated using a long American call and a short American put with the same strike price and expiration.

However, because put-call parity does not hold exactly for American options, this synthetic position is not a perfect substitute for the underlying asset due to the early exercise risk.

Does the Early Exercise Rule Apply Equally to American-Style Put Options?
How Is a Synthetic Short Asset Position Created Using Options?
How Does Early Exercise Affect the Pricing Model for American Options?
Does the Early Exercise Feature Apply to American-Style Put Options as Well?