Updating Your Quote After You Get Hit

You quote 99–101 on something. A trader buys your 101 offer. Now what do you quote next? A surprising number of candidates say "the same thing" — but the trade itself is evidence: someone decided your offer was worth taking, and if any meaningful fraction of your counterparties know more than you do, that decision should shift your estimate of fair value even before you learn anything else about the world.

Why a fill is a signal, not just a transaction

If every counterparty traded for reasons unrelated to value (pure noise), a fill would tell you nothing and your next quote could stay put. But the moment some fraction of flow is informed, a buy at your offer is more likely to have come from someone who believes the true value is above your offer than from someone trading randomly — because informed buyers only buy when it's profitable for them, which means when your offer looks cheap. The fill is a small vote that fair value sits higher than your last midpoint, and rational quoting has to move in response, even with no other news at all.

Worked example

Fair value is 95 or 105, equally likely at the start, so your first quote is centered at 100, say 98/102. Assume 30% of counterparties are informed (know the true value and trade only when profitable) and 70% are uninformed (trade 50/50 regardless of value). Someone buys your 102 offer. Apply Bayes' rule to update the probability that the true value is 105: informed buyers only buy when the value is 105, contributing likelihood 1 for "value=105" and 0 for "value=95." Uninformed buyers buy with probability 0.5 regardless of value, contributing equally to both. Combining: $P(105 \mid \text{buy}) = \dfrac{0.5 \times [0.3(1) + 0.7(0.5)]}{0.5 \times [0.3(1) + 0.7(0.5)] + 0.5 \times [0.3(0) + 0.7(0.5)]} = \dfrac{0.5 \times 0.65}{0.5 \times 0.65 + 0.5 \times 0.35} = \dfrac{0.325}{0.5} = 0.65$. Before the trade, value=105 was 50% likely; after one buy at your offer, it's 65% likely. Your next quote should re-center closer to $0.65(105) + 0.35(95) = 101.5$ rather than staying at 100 — and it should probably widen too, since you've just been shown the flow contains real information.

What this means in practice

This is the logic behind why market makers widen and skew after being consistently hit on one side — a run of buys against your offer isn't bad luck, it's the market telling you where value is. Algorithmic quoting engines automate exactly this Bayesian update, re-centering and re-widening in milliseconds after every fill, which is why prices in liquid markets seem to "walk" in the direction of recent aggressive flow even without any news headline attached.