You quote 19.5 at 20.5 in the 6-month at-the-money option on a $50 underlying, for 200 contracts of 100 shares. A customer lifts your offer. How much theoretical edge did you capture in dollars, and what is left after you pay 0.4 volatility points to lay it off?

You quote 19.5 at 20.5 in the 6-month at-the-money option on a $50 underlying, for 200 contracts of 100 shares. A customer lifts your offer. How much theoretical edge did you capture in dollars, and what is left after you pay 0.4 volatility points to lay it off?

Approach: Convert the quoted width in volatility points into dollars using the vega of the position, then subtract the cost of the offsetting trade in the same units.

$1,414. At-the-money vega is about 0.4*S*sqrt(T) per unit of volatility, so 0.4*50*sqrt(0.5) = 14.14 per share per unit, which is $0.1414 per volatility point per share, or $14.14 per contract. Across 200 contracts the position carries $2,828 of vega per point. Selling on the offer captures half the one-point bid ask spread, so the edge is 0.5*2828 = $1,414. Paying 0.4 points to lay the risk off costs 0.4*2828 = $1,131, leaving $283 of net edge, which is a fifth of the printed edge and the reason a market maker cares more about who else is quoting than about the width on the screen. Quoting in volatility points rather than in premium keeps the edge constant as the underlying moves, since the premium moves with spot while the vega does not.

Follow-up: The customer instead asks for a two-sided market in a 25-delta put. How does the vega per contract change and what extra risk are you taking?

Key concepts: vega, bid ask spread, edge, market making.