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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)

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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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  • $\begingroup$ Thanks. I'm trying to tinker with more variants of such prices to figure out what would be my fair value mid given an orderbook and been seeing a lot of this microprice. $\endgroup$ Nov 16, 2023 at 7:50
  • $\begingroup$ No problem. Just keep in mind this is only one functional form. There's other ways of formulating multi-level microprice. $\endgroup$
    – databento
    Nov 16, 2023 at 8:45

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