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Key Takeaways
- The weighted-midpoint form of microprice weights each quoted price by size on the opposite side.
- A larger bid queue raises the weighted value toward the ask; a larger ask queue lowers it toward the bid.
- The worked $50.00/$50.02 book produces a $50.016 weighted midpoint.
- After 5,000 bid shares cancel, the same calculation gives $50.012.
- Stoikov’s formal micro-price is a separately fitted expected-price construction.
What is microprice?
Microprice is an order-book price estimate that adjusts the midpoint for the sizes quoted at the best bid and best ask. Its common weighted-midpoint form weights the ask by bid size and the bid by ask size, then divides by total size, so a bid-heavy book raises the value toward the ask and an ask-heavy book lowers it toward the bid. The formula expresses the displayed imbalance in price units.
How is microprice calculated as a weighted midpoint?
The example has 8,000 shares bid at $50.00 and 2,000 offered at $50.02. Bid share is 80%, so the calculation is 0.80 × $50.02 + 0.20 × $50.00 = $50.016.
The simple midpoint is $50.010. The $0.006 difference also equals half the two-cent spread multiplied by the signed imbalance of 0.60.
After 5,000 bid shares cancel, bid size is 3,000 and ask size remains 2,000. Bid share is 60%, and the weighted midpoint becomes $50.012. This example shows how size changes the reference while both quoted prices remain fixed.
Formula
Weighted midpoint = (ask price × bid size + bid price × ask size) ÷ (bid size + ask size)- Use positive bid and ask quantities from the same two-sided quote.
- Equivalent form: midpoint + half-spread × signed top-of-book imbalance.
- Signed imbalance = (bid size − ask size) ÷ (bid size + ask size).
- With positive sizes, the weighted midpoint lies between the two quoted prices.
Worked Example
XYZ shows a best bid of $50.00 for 8,000 shares and a best ask of $50.02 for 2,000 shares. The quoted spread is $0.02 and the book is heavily tilted to the bid.
- Bid share of top-of-book size: I = 8,000 / (8,000 + 2,000) = 0.80
- Midpoint: ($50.00 + $50.02) / 2 = $50.010
- Microprice: 0.80 × $50.02 + 0.20 × $50.00 = $50.016
- Same figure as a midpoint adjustment: $50.010 + ($0.02 / 2) × (8,000 − 2,000) / 10,000 = $50.010 + $0.006 = $50.016
- After 5,000 bid shares cancel: I = 3,000 / 5,000 = 0.60, so the microprice is $50.010 + $0.01 × 0.20 = $50.012
The weighted midpoint is $50.016, which is $0.006 above the simple midpoint. After the bid size falls from 8,000 to 3,000, the weighted midpoint becomes $50.012. The bid and ask prices remain $50.00 and $50.02.
Weighted midpoint vs Stoikov’s micro-price
The direct weighted midpoint is one common use of the term. Stoikov’s formal micro-price is a fitted limit of expected future midpoints based on the book state. Research results for that fitted model belong to that construction.
The direct calculation needs the two quoted prices and sizes. With positive sizes, it lies inside their spread. The normalized adjustment from the midpoint is the signed top-of-book imbalance.
How traders use microprice
Read the weighted quote alongside completed executions and the changing market depth. The calculation provides a reference price; the execution record supplies the actual price and quantity.
Limitations of microprice
- The weighted midpoint reads only the best bid, the best ask and their sizes. Read market depth for the levels behind them, and allow for hidden and off-exchange liquidity outside the displayed book.
- Displayed size is free to cancel without a trade. The 5,000-share cancellation moves the value from $50.016 to $50.012 while both quoted prices stay fixed, so recalculate before every order.
- With positive sizes the result always lies inside the spread, less than half the spread from the midpoint: the example’s $50.016 sits between $50.00 and $50.02. For a move beyond the current quote, read depth and executions instead.
- The direct weighted midpoint prices the book as it stands. The short-horizon prediction research covers Stoikov’s fitted model, so use that model when the trade needs a forecast.
Bottom line
Microprice turns the size imbalance at the best bid and ask into a price inside the spread, a finer reference than the simple midpoint. Use it to compare fills with the current book, recalculate it as sizes change, and keep the direct weighted midpoint separate from Stoikov’s fitted model.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- Sasha Stoikov (Cornell): The Micro-Price (presentation slides)
- Cont, Kukanov, Stoikov: The Price Impact of Order Book Events (arXiv:1011.6402)
- Gould, Bonart: Queue Imbalance as a One-Tick-Ahead Price Predictor in a Limit Order Book (arXiv:1512.03492)
- SEC: Market Data Infrastructure Final Rule
How entries are sourced, calculated and updated: editorial methodology.