You are short 1,000 calls struck at 500 on a stock at 500.2, thirty minutes before expiry, hedged with 500 shares. What is your exposure after uncertain exercise, and would you close the position?

The book can wake up anywhere from short 500 to long 500 shares, a 1,000-share swing that rests on other people's exercise decisions. That is pin risk: near the strike at expiry the option's delta is about to jump to 0 or 1, so a hedge sized at 0.54 is wrong either way. Buying back the calls costs about Rs 1,042, mostly time value; I would pay it rather than carry an unhedged position of unknown sign overnight.

Picture a light switch half pressed. It is neither on nor off, but it will be one or the other the moment you let go. An option at the strike at expiry is that switch: its delta is about 0.54 now, but each call ends as either zero shares or one share, never half. The 500-share hedge is right for the blurred state and wrong for both final states. In thirty minutes the stock's typical move is only about Rs 2.2, so the chance of finishing in the money is close to a coin toss, 53%, and the final position depends on which side of 500 the close lands and on what the holders then decide.

Take the cases. All 1,000 exercised: deliver 1,000 shares, hold 500, so short 500 overnight. None exercised: the calls lapse and the 500 shares remain, long 500. Partial exercise is the real danger, because the desk does not learn the number until after the close and cannot trade the stock until morning. If 600 of 1,000 are exercised, it is short 100; if 300, long 200. Each share of error is exposed to the overnight gap, and with 25% volatility a one standard deviation overnight move is about Rs 7.9, so a wrong position of 500 shares carries about Rs 3,939 of one-sigma risk and about Rs 7,877 at two sigma, in a direction nobody knows.

Price the alternative. With thirty minutes left, a call struck at 500 on a stock at 500.2 is worth about Rs 0.99: 0.20 of intrinsic value and about 0.79 of time value. Buying back all 1,000 calls, with a five paise half spread, costs about Rs 1,042, and selling the 500 shares at the same time leaves the book flat with no overnight question at all. That cost is mostly the time value the desk collected when it sold the options, so closing gives back a known amount in exchange for removing an unknown one. On these numbers the trade is clear: pay about Rs 1,042 rather than carry a one-sigma risk of about Rs 3,939 of unknown sign.

Scale and the pin riskThe risk, near expiry, that the stock closes so close to a strike that the option writer cannot know how many options will be exercised, and so cannot know its position. problem grows together: on contracts of 100 shares every rupee figure here is a hundred times larger. Two limits belong in the answer. The buyback price can jump in the last minutes if many writers try to close at once, so desks start reducing pin exposure earlier in the day. And if the stock closes far from the strike, say at 503, exercise is near certain and the right hedge is simply 1,000 shares; the risk is specific to closes within a rupee or two of the strike.