At 10 am on expiry day, Baitarani Capital is short 200 lots (lot 50) of the Satpura 50 22,000 straddle, sold for 60 points, with the index at 22,000. What is the P&L at settlement if the index ends at 21,900, 22,000 or 22,150, and how does gamma behave through the day?

Baitarani makes Rs 6 lakh if the index closes at 22,000, loses Rs 4 lakh at 21,900 and Rs 9 lakh at 22,150. The breakevens are 21,940 and 22,060; every point beyond them costs Rs 10,000. With the index at the strike, the short gamma grows as one over the square root of the time left, from about 106 units a point at 10 am to 352 at 3 pm, so a move in the last hour costs several times what the same move costs in the morning.

At settlement each option is worth its distance into the money and nothing else, so the straddle is worth the distance between the close and 22,000. Baitarani received 60 points and pays the distance, so its P&L per unit is 60 less the distance: at 22,000 it keeps all 60, Rs 6 lakh on 10,000 units; at 21,900 it pays 100 and loses 40 points, Rs 4 lakh; at 22,150 it pays 150 and loses 90, Rs 9 lakh. The breakevens are 22,000 plus and minus 60, 21,940 and 22,060. The shape is a tent, and the loss beyond the breakevens has no floor.

Picture balancing a ruler upright on a fingertip as it gets shorter: a long ruler forgives small wobbles, a short one punishes them at once. For an at-the-money option, gamma is proportional to one over the square root of the time left, so with the index sitting at 22,000 the short straddle's gamma goes from about minus 106 units a point at 10 am to minus 157 at 1 pm and minus 352 at 3 pm, and in the last few minutes it is larger still. In rupees, a 50-point move costs a half times gamma times 50 squared: about Rs 1.3 lakh at 10 am and Rs 4.4 lakh at 3 pm. For an at-the-money straddle the price is close to the expected size of the move to the close, so the market is pricing roughly 60 points either way; the same move is much more expensive late, when it arrives with less time left to recover.

The gamma above is for the index at the strike. Away from the strike the picture flips: at 22,150 with half an hour left the options are deep enough in or out of the money that gamma is close to zero, and the position behaves like a plain short or long index position. So the danger in the last hour is not a large move in itself but the index sitting near 22,000, where gamma is largest, and then moving, because every hedge the desk puts on is wrong a few minutes later. Desks handle this in three ways: buy back the straddle in the early afternoon, giving up the last few points of premium; set a gamma limit that forces a cut when the index is within a band of the strike; or buy cheap far-out options as a cap on the tent. Each costs some of the Rs 6 lakh, which is the price of not losing Rs 9 lakh.

State the limits. The gamma figures come from a simple model calibrated to the 60-point premium and assume trading time runs evenly through the session; real intraday volatility is higher at the open and close. Settlement uses the exchange's closing price method, which may average the last half hour; confirm the current rule. Margin on short index options rises through expiry day as well, and a desk can be forced to cut by its broker before its own limit binds.