As retail traders, it would be difficult to exploit price differences between the synthetic calls / puts versus actual calls / puts. The bid / ask spread would generally wipe out any hope of arb'ing the differences profitably.
However, there may be situations where it may be advantageous to exit your position synthetically, rather than exiting directly.
For instance, let's say you want to exit a deep ITM call option that has a substantial profit. Since the call option is deep ITM, the bid/ask spread may be quite wide. If you were to close the call option, you may lose a bit of profit on the bid / ask spread.
So instead of selling the call option, you can synthetically close the call option by shorting the stock directly. Since the stock would likely have a tighter bid / ask spread, you would give up less profit than if you were to sell your deep ITM call option.
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