Pin risk is what happens when a stock closes right at the strike of an option you sold at expiration. The option might or might not get exercised. You cannot tell at the close. You find out Monday morning when your broker either delivered you shares or did not.
That uncertainty is the risk. By Monday the stock could have gapped against the position you did not know you had.
You sold a $50 strike put. Stock closes at $50.02. Technically the put is one cent in the money. But the long holder may or may not exercise. Some will. Some will let it expire because the gain is too small to bother. Brokers auto exercise anything in the money by a penny, but only on the long side they hold.
Result: you might wake up Monday with 100 shares at $50, or you might wake up flat with the premium kept. The market opens Monday and the stock might gap to $48 (if assigned, you are immediately down $200 per contract) or jump to $52 (you missed the gain if not assigned).
Any short option within fifty cents of the strike going into the expiration close gets closed. Period. The cost to close is cheaper than the operational risk of holding through the weekend.
If a position is right at the strike with thirty minutes to expiration and the cost to close is small, I close. If the cost to close is more than I am willing to pay, I close anyway because the alternative is worse.
Friday expiration of weekly options. The stock pinned right at your strike. You assumed it would close above or below clearly. It did not. Sunday night the company drops news. Monday open is a different stock.
End of quarter and end of year expirations. Higher volume on these dates means dealer hedging pressure is stronger. Pinning at round strikes is more common.
Say you collected $1.50 on a put. The stock closes right at the strike. Bid to close is $0.10. You pay $10 to remove the position. Net profit is $140 instead of $150. You give up $10 to eliminate the assignment risk entirely. That is a great trade. The $10 is insurance.
Holding to find out is gambling. The expected value is negative once you account for weekend gap risk.
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