Quoting a Price Is Writing Free Options: Copeland and Galai on Adverse Selection

Here is a thought that should make any market maker slightly ill.

When you post a bid and an ask, you are making a public promise. You are telling the entire world: whatever happens, whatever you know that I do not, for the next moment I will buy at this price and sell at that price. Anyone may take you up on it. You cannot ask them why.

Copeland and Galai looked at that promise in 1983 and recognized it for what it is. You have just written two options and given them away for free.

The problem: the people trading against you are not all the same

Split the world into two kinds of traders.

The first kind trades for reasons that have nothing to do with the stock's value. They need cash for a house deposit, they are rebalancing a pension fund, they are hedging. Call them liquidity traders. Trading against them is lovely. Half of them buy from you, half sell to you, and you collect the spread on both sides. They are the customers who pay your rent.

The second kind knows something you do not. Maybe they have done the work, maybe they have a faster feed, maybe they are just plain informed. Call them informed traders. They will only trade against you when your price is wrong in their favour. They buy from you when your ask is too low. They sell to you when your bid is too high. You never win against them. Not on average, not ever, by construction.

The market maker's problem is that both types show up looking exactly the same. There is no name tag on an order.

The key idea via analogy: the free option you cannot take back

Copeland and Galai's contribution was to make the analogy precise, and once you see it, you cannot unsee it.

Your posted ask is a call option you have written and given away. If the true value turns out to be above your ask, an informed trader exercises it, buying from you cheap. If the true value is below your ask, nobody informed touches it, and you gain nothing from having offered it.

Your posted bid is a put option you have written and given away. If the true value falls below your bid, an informed trader exercises it, dumping stock on you at a price above what it is worth.

So the market maker is short a straddle, permanently, for free, to a counterparty who may be smarter than them. In options language, that is a horrifying position. Options have value, and you are handing that value out at zero premium.

Except you are not, quite, because the spread is the premium. The whole point of the spread is to be wide enough that the money you make from the liquidity traders covers the value of the options you are giving to the informed ones. Set it too tight and the informed traders bleed you dry. Set it too wide and the liquidity traders stop coming and you have no revenue at all. The optimal spread is the one that maximizes the difference between what you collect from the innocent and what you lose to the informed.

Framing it as options is not just cute. It lets you borrow the entire option pricing toolkit to reason about spreads, and it immediately delivers predictions:

• More volatile stocks should have wider spreads. Options on volatile things are worth more, so giving them away for free costs you more, so you must charge more. This is exactly the intuition from Black and Scholes applied in a place nobody expected it.
• Spreads should be narrower when trading is heavy and continuous. More liquidity trader volume means more premium collected against the same option giveaway.
• More competition among market makers should compress the spread, but only down to a floor, because the adverse selection cost is not profit that competition can compete away, it is a real loss that has to be funded.

Why it mattered

• It made adverse selection the second pillar of microstructure. Stoll and Ho had built the inventory story: spreads exist because dealers get stuck with unwanted risk. Copeland and Galai built the other pillar: spreads exist because dealers get picked off. Everything that followed, Glosten and Milgrom, Kyle, PIN, VPIN, "order flow toxicity," is an elaboration of this pillar.
• It explains a fact the inventory story cannot. Why do spreads widen dramatically right before an earnings announcement, when trading is calm and inventories are normal? Inventory risk has not changed. What has changed is that the chance the next person knows something has spiked. Only the adverse selection story predicts that.
• It gave "informed trading" an economic price tag. The insight that the cost of being on the wrong side of information is literally an option premium is the reason modern desks talk about toxic flow and try to measure it. The vocabulary of "getting run over," "adverse selection cost," and "flow toxicity" all trace back to this framing.
• It reframed the spread as a defence, not a rent. That distinction matters enormously for policy. If the spread is a monopolist's margin, regulate it away. If it is a defence against being picked off, regulating it away means nobody quotes.

The honest limitations

• The information structure is stylized. Traders in the model are either fully informed or completely uninformed, and the split is fixed. Real markets have a continuum of partial information, and the proportion of informed flow moves around constantly.
• The market maker never learns. In this setup, the dealer sets a spread and absorbs the losses. They do not do the thing real dealers do, which is update their beliefs after seeing the trade. If someone just bought a lot from you, that is evidence. Glosten and Milgrom's model, published two years later, made exactly that fix by having the market maker revise quotes based on the trade they just saw, which is why it, rather than this paper, became the canonical adverse selection model.
• It says nothing about how information gets into prices. The paper explains the cost of informed trading to a dealer. It does not explain how the informed trader chooses their order size, or how the market's price eventually converges on the truth. Kyle's continuous auction model took on that side.
• The option analogy is a metaphor with hard edges. The "options" here have no fixed maturity and no clear exercise boundary, and the informed trader's decision to exercise is strategic in ways a standard option holder's is not. The metaphor buys you enormous intuition, but you should not push the pricing formulas too literally.

The one-line takeaway

Copeland and Galai showed that every quote you post is a free option written to whoever might know more than you, so the bid-ask spread has to be wide enough that ordinary traders pay you the premium the informed ones are collecting for nothing.