A desk holds 400 lots, lot 50, of index calls with delta 0.45, gamma 0.0002 per point and vega Rs 12 per vol point per unit, index at 22,000. Express delta in index units and rupees, gamma as the change in rupee delta for a 1% move, and vega in rupees per vol point.

The book's delta is 9,000 index units, Rs 19.8 crore of index exposure or 180 lots of futures; a 1% move changes that delta by 880 units, about Rs 1.94 crore; and vega is Rs 2.4 lakh per vol point. The book holds 20,000 option units. Delta times 20,000 gives index units; times 22,000 gives rupees. Gamma times 20,000 gives 4 units per point, and a 1% move is 220 points.

A car's speed can be 60 kilometres an hour, 1 kilometre a minute or 16.7 metres a second; nothing about the car changes, only the unit. A Greek on a pricing screen is per unit of one option; the risk officer wants it for the whole book and in rupees, and the hedger wants it in lots of futures, so the same risk has to be read three ways. Start by counting: 400 lots of 50 is 20,000 option units. Every conversion below is that count times the screen figure, then times the index level if the answer is wanted in rupees.

Multiply 20,000 units by 0.45 and the book behaves like 9,000 units of the index. In rupees that is 9,000 times 22,000, Rs 19.8 crore of index exposure, and to hedge it the desk would sell 9,000 divided by 50, or 180 lots of futures. For a 1% rise of 220 points, delta alone makes 9,000 times 220, Rs 19.8 lakh, which is just 1% of the rupee delta, a quick check that the conversion is right.

Per option, each index point adds 0.0002 to delta. Across 20,000 options that is 4 index units of delta per point. A 1% move is 220 points, so the book's delta grows by 4 times 220, 880 index units, which at 22,000 is about Rs 1.94 crore of extra exposure. That is why desks quote gamma per 1% move in rupees: a figure of 0.0002 sounds negligible and Rs 1.94 crore of new delta on an ordinary day does not. The extra profit from gamma on that 1% move is half of 4 times 220 squared, Rs 96,800, small next to delta but it grows with the square of the move.

Vega is already in rupees per option, so only the count matters: Rs 12 times 20,000 is Rs 2.4 lakh for each point of implied volatility. If volatility rises from 14% to 16%, the book gains about Rs 4.8 lakh before any index move. The limitation to state is that every figure here is a snapshot: delta, gamma and vega all change as the index and volatility move and as expiry approaches, so the summary carries the time it was taken and is redone at the next close.