Extending Microprice to Multiple Order Book Levels

Summary

The document describes a way to extend the standard top-of-book microprice to several price levels. At each level, it weights the ask price by bid-side size and the bid price by ask-side size, then divides the combined weighted prices by total depth across both sides. This gives greater influence to prices opposite the displayed volume imbalance.

It presents the formula as a straightforward generalization of the level-one calculation, but provides no empirical tests or comparison with other multi-level estimators. The result depends on which levels are included and on the depth and prices recorded there; the note does not discuss how to handle sparse books, changing depth, or whether this estimator predicts future prices better than alternatives.

Key ideas

• A top-of-book microprice uses opposing-side sizes to weight bid and ask prices.
• A multi-level version sums the opposing-size-weighted prices across the included levels.
• The denominator is the combined bid and ask depth over those levels.
• The document proposes the estimator without evidence about predictive performance.

Tags

# Multi level micro price


# Multi level micro price












Typical micro price formula uses the top of book depth (i.e. level 1 depth):

> Microprice = (BidSize x AskPrice + AskSize x BidPrice) / (BidSize + AskSize)

But how does one actually include more depth levels (e.g. top 3 levels)?

> Multi-level Microprice = (TotalBidSize x AskVwapPrice + BidVwapPrice x TotalAskSize) / (TotalBidSize + TotalAskSize)

## Answer by databento (score 2, accepted)

https://quant.stackexchange.com/a/77380

Naive way of doing it: weight each price by the depth of the opposing side.

$$\text{p}\left(n\right){\displaystyle =}\dfrac{\sum_{i=0}^{n}\left(s_{b,i}p_{a,i}+s_{a,i}p_{b,i}\right)}{\sum_{i=0}^{n}\left(s_{b,i}+s_{a,i}\right)}$$

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.