The microprice

A fair-value estimate that weights the bid and ask by the opposite side’s size, so it leans toward the heavier queue. A better one-step-ahead predictor than the mid, and the money-ladder’s bottom rung.

See it move

What is the microprice?

The microprice is an estimate of an instrument's fair value that corrects the mid-price for order-book imbalance. The mid (halfway between the best bid and the best ask) pretends both sides of the touch are equally strong. They rarely are. If 5,000 lots rest on the bid and only 200 on the ask, that wall of buyers is about to consume the thin offer and tick the price up, so a fair value that ignores the imbalance sits too low: it is biased toward the heavy side's victim, not its winner.

The microprice (Stoikov 2018) is the mid plus a correction for which way the book is leaning. The payoff is that you can learn to read imbalance off a book by eye: glance at the size on each side of the touch and you can call the likely direction of the next print before any trade happens. The microprice is the formalisation of that instinct, and it is the price a modern market maker actually quotes around.

It is the empirical partner of order-flow imbalance: OFI measures the flow of imbalance (events over a window) to predict the next move; the microprice reads the static imbalance (the sizes resting now) to set a fair value. Same information, the lopsided book, used for the two halves of a maker's job: where to centre quotes (the microprice) and when to widen (OFI and toxicity).

Mid, weighted-mid, or microprice?

There are three fair values you can read off the top of the book, and they treat imbalance very differently. The mid-price ignores size completely. A book with 5,000 × 200 has the same mid as one with 200 × 5,000, even though those two books predict opposite next moves, so the mid is plainly wrong as a fair value whenever the book is lopsided.

The weighted-mid is the linear correction. It weights each side's price by the opposite side's size, so a big bid pulls fair value toward the ask (up). Writing imbalance as $I = Q_b/(Q_b+Q_a)$, the weighted-mid moves linearly in $I$: at $I=0.5$ it is the mid, at $I=1$ it is the ask, at $I=0$ it is the bid. Better than the mid, but the linearity is wrong: real books do not forecast the next move as a straight line in imbalance.

The microprice is Stoikov's empirically-correct adjustment. It replaces the linear weighting with a fitted, S-shaped function $G(I)$ that is flat near $I=0.5$ (a balanced book barely moves fair value off the mid) and steep near the edges (a near-one-sided book snaps fair value almost to the touch). Near balance, small imbalance fluctuations are noise and should not jerk your fair value around; near a one-sided book the imbalance is real, persistent, and about to resolve. The linear weighted-mid over-reacts in the middle and under-reacts at the edges, exactly backwards; the microprice gets both right because it is fitted to how imbalance actually forecasts the next move.

The weighted-mid is just the microprice with a straight line, $G(I) = 2I-1$, in place of the fitted S-curve. That single substitution is the whole difference between the naive estimator and the principled one.

Why does a market maker quote around the microprice?

A maker quoting symmetrically around the mid systematically posts its bid too high and its ask too low whenever the book is imbalanced, feeding the very flow that is about to pick it off. If the book is bid-heavy ($I=0.8$) the price is about to tick up, but a maker centred on the mid has its ask too cheap: it gets lifted right before the uptick, a textbook adverse-selection loss. Centre on the microprice instead and the ask is pulled up toward where price is going; the maker is no longer the cheapest stale offer in a rising book.

This is the fair-value half of the modern maker's quote. A production maker quotes around the microprice, then skews for inventory (the Avellaneda–Stoikov reservation price), with a half-spread covering inventory cost plus an adverse-selection term: the combined rule of the order-flow & information guide. The microprice is what replaces the naive mid as the centre of that quote: the single most direct way a better fair value turns into fewer toxic fills and more captured spread.

It is also a toxicity signal in disguise. A microprice that has pulled far from the mid is a book screaming that one side is about to win. A maker watches the microprice-minus-mid gap the way it watches OFI and VPIN, as a reason to widen, skew, or pull on the exposed side.

Why is the microprice the right fair value?

The naive weighted-mid is an ad hoc blend; the microprice is a target. Stoikov defines it as the expected future mid-price, conditioned on the current imbalance and spread, pushed far enough ahead that the current imbalance has washed out. The one-line intuition: the microprice is your best guess of the mid a few ticks from now, given how lopsided the book is right now.

That construction gives the microprice the martingale property: once you are standing at the microprice, the expected next change is zero, because all the predictable drift from the current imbalance has already been priced in. The mid lacks this: from the mid, the expected next move is not zero when the book is imbalanced; it drifts toward the heavy side. This is also why the adjustment is S-shaped rather than linear: the conditional expectation of the future mid is naturally flat near balance (imbalance near 0.5 carries little forecast) and steep near the edges (extreme imbalance strongly forecasts the resolving move). The $G(I)$ curve is that conditional expectation, estimated from data, not a chosen functional form.

Honest scope note. The construction assumes $(I, S)$ is a useful, roughly-Markov summary and that imbalance mean-reverts: good approximations in many markets, weaker in very thin books or gappy prediction markets. The principle (fair value = martingale conditional on book state) is general; the fitted $G$ is venue-specific and must be re-estimated, not copied. That is the 2026 edge: a well-fitted $G$ on your venue beats the textbook one.

Worked example

Take a synthetic two-level book, as of 2026; reproduce it in the interactive above. The best bid is 100.00 and the best ask 100.02, so the spread is $S = 0.02$ and the half-spread is 0.01. Bid size is $Q_b = 800$ lots, ask size $Q_a = 200$ lots, giving imbalance $I = 800/1000 = 0.80$ (strongly bid-heavy). Now read the three fair values off that single book.

The mid is $(100.00 + 100.02)/2 = 100.010$, ignoring the 4:1 imbalance entirely. The weighted-mid is $(100.02 \cdot 800 + 100.00 \cdot 200)/1000 = 100.016$, pulling fair value 0.6 of the way to the ask, linearly in $I$. The microprice uses the S-shaped curve: at $I=0.80$ a fitted adjustment might give $G(0.80) \approx 0.78$, steeper than linear out near the edge where imbalance strongly forecasts the move, so $p^{\text{micro}} = 100.010 + 0.01 \cdot 0.78 \approx 100.018$, higher than both the mid and the weighted-mid, because an $I=0.8$ book reliably resolves upward.

The maker's takeaway. A maker centred on the mid (100.010) quotes an ask near 100.015, too cheap; it gets lifted just before the uptick (adverse selection). A maker centred on the microprice (100.018) quotes its ask near 100.023, so it is not the stale cheap offer and is picked off far less, and when it does fill it is nearer true fair value. Same spread width, very different realised P&L. That difference is the money the better fair value earns.

The forecast-error check. Track each estimator's error against the realised next mid-move over the synthetic tape. With informed flow turned on, the average squared error ranks $\text{microprice} \lt \text{weighted-mid} \lt \text{mid}$: the S-shaped estimator wins because it neither over-reacts near balance nor under-reacts near the edge. That is the martingale property made measurable.

Now balance the book. Set $Q_b = Q_a = 500$ so $I = 0.5$. All three collapse to the mid (100.010): with no imbalance there is nothing to forecast, and $G(0.5) = 0$. The microprice's advantage is entirely in imbalanced books, which, on real venues, is most of the time. The numbers here are synthetic and rounded; the adjustment $G(I)$ must be fitted per instrument and venue and dated, because the textbook curve is a starting point, not a deployable parameter. The principle is robust; the fitted curve is where the edge and the work are.