Vairatgad Market Makers quotes one-month options on Chandoli Paper. An at-the-money option has vega of Rs 1.2 per vol point per share, fair volatility is uncertain by about 0.8 points, and hedging costs about Rs 0.10 a share. What is a minimum sensible bid-offer width, and what would make you widen it?

About Rs 2.12 wide: bid Rs 34.86, offer Rs 36.98 around a fair value of Rs 35.92. Each side covers Rs 0.96 of volatility uncertainty, vega of 1.2 times 0.8 points, plus Rs 0.10 of hedging cost. Widen when the uncertainty grows, before earnings or in a fast market; move the middle of the quote rather than its width when inventory is heavy on one side.

A money changer at an airport quotes a buying rate and a selling rate. The gap is not greed alone: she does not know exactly where the currency will be by the time she has to sell what she buys, and she pays costs to restock. An option market maker's width pays for the same two things: the chance that its estimate of fair value is wrong, and the cost of hedging what it has just traded. For an option the uncertain input is volatility, and vega converts volatility uncertainty into rupees: with vega of Rs 1.2 a point and an estimate good to 0.8 points, fair value is uncertain by about Rs 0.96 a share. Quote tighter than that and the counterparties who know more than the desk will pick it off, which is called adverse selectionThe tendency of a quote to be hit by traders who have better information than the quoter, so trades that go through are more often the losing ones..

Build it outward from fair value, one side at a time. On the offer, add Rs 0.96 for being wrong on volatility and Rs 0.10 for buying the delta hedge, Rs 1.06; do the same on the bid; the quote is Rs 34.86 bid, Rs 36.98 offered, Rs 2.12 wide. That is about 6% of the option's price, typical for a single-stock option that is liquid but not the most active in the market. It is a floor, not a target: it assumes the desk breaks even on average, so any profit has to come from capturing the width on both sides more often than the desk is picked off.

Widen when the inputs to the width grow. Before an earnings date the desk might know fair volatility only to within 2.5 points, and the same arithmetic gives Rs 3.00 plus Rs 0.10 a side, a width of Rs 6.20, more than three times the ordinary quote. The same applies in a fast market, when the stock gaps faster than the hedge can follow, and in thin stock liquidity, when the hedging cost rises. Inventory is different. If the desk is already long a lot of Chandoli volatility, it does not want more, so it lowers both bid and offer, say by Rs 0.30, to make selling to it less attractive and buying from it more attractive. Widening in that case would make the desk less likely to trade at all, when what it wants is to trade one way.

State the limits. The width here is for one at-the-money option; out-of-the-money options have less vega and a smaller absolute width, but often a wider percentage width because their volatility is less certain. The exchange's obligations for a designated liquidity provider set a maximum width, confirm the current rule, and when the arithmetic says wider than that, the desk must either accept the risk or reduce size. And the 0.8-point uncertainty is itself an estimate: a desk that has been picked off five times in a morning should conclude its fair volatility is wrong, not that it was unlucky.