Kalyangad Capital runs a delta-neutral short Satpura 50 options book with gamma of minus 2 units per point and vega of minus Rs 5 lakh per vol point, index at 22,000. Stress it for a 10% gap down with volatility up 10 points. Why does the Greek estimate understate the loss?

The Greeks say about Rs 98.4 lakh: Rs 48.4 lakh from gamma and Rs 50 lakh from vega. Full revaluation says about Rs 153 lakh. The Greeks are slopes measured at 22,000 and today's volatility; the short 20,000 puts gain gamma and vega as the index falls toward them and as volatility rises, so the true loss curves away from the estimate. A 10% gap is far outside the range where a slope is a good map, which is why stress tests reprice every option.

Start with the estimate a risk report gives. The book is delta neutral, so the first-order move costs nothing. A 10% gap is 2,200 points. The gamma term is a half times gamma times the move squared: a half times minus 2 times 2,200 squared is minus Rs 48.4 lakh; the vega term is minus Rs 5 lakh times 10 points, minus Rs 50 lakh; the estimate is minus Rs 98.4 lakh. This is the second-order Taylor expansion every desk uses for small moves, and for a 1% move it would be close to exact.

Think of judging a hill from the slope under your feet. On a gentle rise that works for a few steps; walk a kilometre and the slope you measured at the start tells you little about where you end up. Gamma and vega are slopes measured at 22,000 and 15.5% volatility, and for a 20,000 put both grow as the index falls toward the strike and as volatility rises, so each further point of fall costs more than the last. Reprice every put at 19,800 and the new volatility and the loss is about Rs 153.3 lakh, 1.56 times the estimate. Split it: the index fall on its own costs Rs 70.0 lakh against gamma's Rs 48.4 lakh; the volatility rise on its own costs Rs 62.7 lakh against vega's Rs 50 lakh; and the two together cost a further Rs 20.6 lakh, because a put that is suddenly near the money has far more vega to lose when volatility jumps. Traders call that cross term vannaThe rate at which an option vega changes as the underlying moves, or equivalently how delta changes as volatility moves. For out-of-the-money puts it makes a fall and a volatility rise compound..

Run the same comparison for gaps from zero to 15%, with volatility rising one point for every 1% fall. For a 2% gap the two numbers are close; by 10% the full loss is about 1.6 times the estimate, and by 15% the index is through the strike and the gap widens further. That is why clearing houses and risk teams set margins and limits on scenario grids that reprice every position across a range of index moves and volatility shifts, rather than on Greek sums, and why a desk that only watches its Greek report finds out about the shape of its book on the worst night of the year.

Close with what you would tell the committee. The book's stress loss is about Rs 153 lakh, not Rs 98 lakh, and the gap between the two comes from the strikes sitting 9% below the index, exactly where a crash takes them. Buying a smaller number of further out-of-the-money puts, say at 18,500, would cap the tail at a cost in premium income. State the limits: the scenario holds volatility flat across strikes, while in a real sell-off the skew steepens and the 20,000 puts' volatility rises by more than the at-the-money 10 points, and the futures hedge assumes the market can be traded at 19,800, which on a gap open it often cannot.