A customer buys 500 one-month at-the-money index calls from Mayurika at Rs 12 (delta 0.5, gamma 0.013 per rupee, vega Rs 1.1 per vol point, per unit of index). Mayurika hedges the delta; then the index jumps Rs 10 and implied volatility rises 2 points. What is the P&L, and what is the new hedge?

Mayurika loses about Rs 1.42 lakh: Rs 32,500 to gamma and Rs 1.10 lakh to vega, while the 25,000-unit futures hedge exactly offsets the delta part. Full repricing gives Rs 1.45 lakh. The edge of Rs 20,000 covered about a seventh of it. After the move the call delta is about 0.62, so the hedge must grow to about 30,800 units: buy 5,800 more futures.

Short 50,000 units of calls with delta 0.5 behave, for small moves, like being short 25,000 units of the index. So Mayurika buys 25,000 units of index futures, which makes the book flat to a small move in either direction. Think of it as the desk selling an insurance policy on a rise and then buying enough of the thing insured to be indifferent to a nudge. Indifference to a nudge is not indifference to a shove, and that difference is what the rest of the case measures.

Expand each call's value change into its parts. The delta part is 0.5 x 10 = Rs 5.00. The gamma part is half of gamma times the move squared, 0.5 x 0.013 x 100 = Rs 0.65. The vega part is 1.1 x 2 = Rs 2.20. Each call gains about Rs 7.85, and Mayurika is short all of them: a loss of Rs 3.925 lakh on the calls, of which Rs 2.5 lakh is returned by the futures. The remainder is the cost of being short convexity and short volatility at the same moment, which is how a short option position usually loses: the news that moves the index also makes options dearer.

Check the expansion by repricing. At the implied volatility of 10.5% that makes a one-month at-the-money call worth Rs 12, the call is worth Rs 19.91 at an index of 1,010 and volatility 2 points higher, a change of Rs 7.91, close to the Rs 7.85 from the Greeks. The exact loss is Rs 1.455 lakh; the expansion is good enough to trade on and slightly understates the loss.

Gamma says delta rises 0.013 for each rupee, so after Rs 10 it is about 0.63. The higher volatility flattens the delta curve a little, and full repricing gives 0.62. Mayurika is now short about 30,800 units of delta and holds only 25,000 units of futures, so it must buy about 5,800 more, at the higher price. That is the mechanical cost of short gamma: the hedger buys after rises and sells after falls. If the customer's flow keeps coming, the desk also reprices: its quotes for the next calls should be higher in volatility, because its own book is now shorter vega than it wants.

The limitation to state: the Greeks are local, a Rs 10 move in one jump is well beyond a typical day for an index with volatility near 10%, and a desk sizes such a position by stress scenarios of jump and vol together, not by the Greeks alone. The edge earned at the trade is small next to one bad jump, which is why short-gamma books carry gamma and vega limits.