After selling calls to a client, your desk must buy 2 lakh shares to hedge delta. Mid is 500.5 and the offers are 20,000 at 501, 40,000 at 502, 60,000 at 503 and 80,000 at 505. What are the average fill and the slippage if you sweep the book, and what else could you do?

Sweeping the book fills 2 lakh shares at an average of Rs 503.40, Rs 2.90 above the 500.5 mid, a cost of about Rs 5.8 lakh. The alternatives are to take the cheap levels now and work the rest over the day, to hedge with stock futures if they are more liquid, or to accept some unhedged delta for a while. Each swaps a known impact cost for price risk on Rs 10 crore of exposure. The lasting lesson is that this cost belongs in the option's price.

Buying a hundred tickets for a sold-out concert is the everyday version. The first few resellers ask a little over face value, the next ask more, and the last pair costs the most, because you have used up the cheap supply. An order book works the same way: each level is a seller at a price, and a buy order larger than the best offer eats through level after level, so the average price is a size-weighted average that sits well above the first offer. Here that is 20,000 times 501 plus 40,000 times 502 plus 60,000 times 503 plus 80,000 times 505, Rs 10.068 crore for 2 lakh shares, or Rs 503.40 each.

The sweep's cost is known; the alternatives replace it with risk. Waiting to hedge saves impact but leaves the desk short delta on about Rs 10 crore of stock, and if the stock moves 2% in a day, an assumption to check against its history, one standard deviation of that move over an hour is about Rs 8 lakh, more than the whole sweep cost. So the choice is between a certain Rs 5.8 lakh and an uncertain amount with a zero average and a wide spread.

Before the trade. The client bought calls with a delta of 2 lakh shares, about 4 lakh options at a delta of 0.5. Sweeping costs about Rs 1.45 per option just for the first hedge, and the hedge will need rebalancing as the stock moves, each time against the same thin book, so the desk should price that cost into the option's offer. A desk that quotes options on a thin stock off the screen mid, as if hedging were free, gives this money away on every trade. In practice the answer is usually a blend: take the cheap levels, show a working order on the rest, watch whether new sellers refill the book, and keep the open delta inside a limit agreed in advance. Say the limit of the analysis too: the visible book is not the whole supply, and hidden or refilling sellers can make patient buying cheaper than the screen suggests, or more expensive if others are buying too.