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Using Mid-Price and Microprice as Fair-Value Regression Targets

Article Quant Q&A · Author: Accelerate to the Infinity
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Summary

The document asks how a market maker could train a regression model to estimate fair value when the target label is not directly observed. The accepted answer explains that a fair-value proxy can be calculated from current order-book data: the mid-price averages the best bid and ask, while the microprice weights those quotes using the displayed volumes at each side. With bid, ask, and top-of-book volume data available, either value can serve as a regression target; the answer suggests the talk likely referred to microprice.

These definitions provide practical target construction for supervised estimation, but the text does not specify model features, training labels over time, validation, or evidence comparing prediction quality. The microprice is an observable proxy derived from the book, not proof of an asset’s uniquely correct intrinsic value. Its suitability depends on the market-making task and the data available.

Key ideas

  • A regression target for fair value can be constructed from observed order-book quotes and volumes.
  • The mid-price is the simple average of the best bid and best ask.
  • The microprice weights bid and ask prices according to displayed volume on each side.
  • The answer suggests that microprice was probably the fair-price measure intended in the market-maker talk.

Tags

Market makingMarket microstructureExecutionStatistics
Full text
# Fair Value Regression Methods


# Fair Value Regression Methods












Recently we had an invited talk at our university (I'm Ph.D. student in ML department, so I'm sorry if my question is stupid, since I do not have quantitative finance background), where one researcher from large market maker company was talking about what they do, and he mentioned fair value estimation for bid-ask spread as one of the problems. In his talk, he explained quite well what it is and how it is used in practice and he mentioned that "simple regression method does it quite well".

What I was wondering is, how can one use "simple regression" to regress fair value? That would assume that one can assign post-factum fair value in the dataset but I can't come up with the solution on how can one assign this value so easily and would guess that such kind of a problem would be better solved using optimal control problems.

Are there any good academic papers that deal with fair value regression and would probably answer my question?

Thanks!

## Answer by Accelerate to the Infinity (score 2, accepted)

https://quant.stackexchange.com/a/61376

So after some time I found what was meant by the "fair price" in the context of the speakers presentation.

Since in the data one knows $P^b, P^a, V^b, V^a$, i.e. best bid/ask price, and best bid/ask volume at the current time, one can consider the following definitions of fair value:

- Just a mid-price, i.e. $P = \frac{1}{2}(P^b + P^a)$

- Microprice (also known as weighted mid-price), i.e. $P = \frac{V^b}{V^a + V^b}P^a + \frac{V^a}{V^b + V^a}P^b$

With high probability the presenter was speaking about microprice, and since the potential market maker has access to the order book depth dataset, the question on estimation of the regression target is easy.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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