A long volatility book made Rs 12 lakh yesterday. At the open it had delta of plus 2,000, gamma of 150 per point, vega of Rs 3 lakh per point and theta of minus Rs 4 lakh a day. The index rose 60 points and implied volatility 1.5 points. Explain the P&L and size what is unexplained.

The Greeks explain Rs 4.4 lakh of the Rs 12 lakh, leaving Rs 7.6 lakh unexplained. Delta made Rs 1.2 lakh, gamma Rs 2.7 lakh, vega Rs 4.5 lakh and theta cost Rs 4 lakh. An unexplained piece of 63% is too large to accept: the likely sources are the skew moving more than the at-the-money point, the cross-Greeks, intraday hedges, and trades booked late, in that order of where to look first.

Think of a shopkeeper closing the till. Sales explain most of the cash, the rent explains a deduction, and whatever is left over is either a mistake in the count or something nobody wrote down. The Greeks are the till count for an options book. Delta earns the move times the position: 2,000 units times 60 points is Rs 1.2 lakh; gamma earns half the gamma times the move squared, Rs 2.7 lakh; vega earns Rs 3 lakh for each of the 1.5 points, Rs 4.5 lakh; theta costs one day, Rs 4 lakh. The sum is Rs 4.4 lakh. Every term uses the Greeks as they stood at the open, which is the first thing to remember about the method's limits.

Go through the sources in the order they usually matter for a long volatility book on an up day. First, the volatility input: the attribution used the at-the-money rise of 1.5 points, but a long book is rarely all at the money, and if the book holds out-of-the-money puts whose implied volatility rose 3 points as the skew steepened, the true vega gain is well above Rs 4.5 lakh. Second, the cross-GreeksSensitivities to two things moving together. Vanna is how delta changes with volatility; volga is how vega changes with volatility.: with the index up and volatility up, vanna and volga can each add a few lakh on a book this size and neither is in the four-term formula. Third, the day itself: the Greeks were measured at the open, and if the trader rehedged delta at midday the gamma term is really a sum of smaller pieces, and if a trade was booked at a stale price the P&L is simply wrong. The residual is not profit until each of these has been sized.

Rerun the attribution with the volatility move at each strike rather than the one at-the-money number, and with vanna and volga included; a good risk system does this by full revaluation. If the rerun explains Rs 10 or 11 lakh, the day is understood and the residual is noise; if it still leaves Rs 5 lakh unexplained, hold the number, reconcile the blotter against the exchange, and check every trade booked after 2 pm. Then say the limit of the method: the Greeks are local, built for small moves at opening values, so a 60-point day with a volatility jump will always leave something behind, and the question is only whether the something is small enough to live with. A trader who reports Rs 12 lakh with Rs 7.6 lakh unexplained and no reconciliation is reporting a guess.