A fund holds 1,000 lots of six-month at-the-money calls on a stock at 500 when the company announces a surprise special dividend of Rs 25, payable in two months. With delta 0.55, estimate the loss, and explain why put holders gain.

The calls lose about Rs 12.75 a share, roughly Rs 12.75 lakh on the position, because the dividend lowers the forward by about Rs 25. Delta alone gives 0.55 times 25, Rs 13.75 a share; gamma gives back about Rs 1.00. Puts gain by the mirror logic, about Rs 12.25 a share. If the exchange adjusts contract terms for extraordinary dividends, the loss largely disappears, so check that first.

Think of a flat you have an option to buy in six months at a fixed price. The owner announces he will strip out the kitchen and sell it separately before then. The flat you can buy is now worth less, even though nobody has touched it yet. A call is an option on the stock at expiry; the stock will drop by about the dividend on the ex-date, and only shareholders receive the cash, so the forward priceThe price agreed today for buying the stock on a future date. It equals spot plus interest, less dividends paid before that date. falls by about Rs 25 the moment the dividend is announced. Ordinary dividends are already in the forward; a special dividend is a surprise, which is why it moves the option today.

First order, the call moves by delta times the change in the forward: 0.55 times minus 25 is minus Rs 13.75 a share. On 1,00,000 shares that is about Rs 13.75 lakh, and gamma trims it a little, because the delta falls as the forward falls. The second-order term is half of gamma times the move squared: 0.5 times 0.0032 times 625, about Rs 1.00. The better estimate is Rs 12.75 a share, about Rs 12.75 lakh. A full revaluation in the pricing model, with the dividend input changed, is what the desk would book; the Greeks are the estimate you give before the open. The interest on Rs 25 for the four months between payment and expiry is ignored here; it would change the answer only by paise.

Put-call parity ties the two together: a call minus a put on the same strike equals the forward minus the strike, discounted. If the forward falls by Rs 25 and the strike does not move, call minus put must fall by about Rs 25, and the put's delta of minus 0.45 takes the other part: it rises by about 0.45 times 25, Rs 11.25, plus the same gamma cushion, about Rs 12.25. Add the call's loss and the put's gain and you get about 25, as parity says. Whoever wrote Ghataprabha's calls has gained what the fund lost, and anyone short puts has lost.

Many exchanges treat a large one-off dividend as a corporate action and adjust the strikes, and sometimes the lot size, of listed options so that holders are left whole. The dividend here is 5% of the share price, so the first question is whether the exchange's corporate action policy classes it as extraordinary. The threshold and the method are set in each exchange's rules and change from time to time; confirm the current rule rather than relying on a remembered number. If the strike is cut by Rs 25, the calls are roughly unaffected. If the dividend falls below the threshold, or the options are over-the-counter without an adjustment clause, the loss stands, and the limit of any Greeks estimate applies: it is an approximation, good for a small move and a first call to the portfolio manager.