The microprice, when the mid lies

Question

The top of book shows: bid 100 with 900 shares resting, ask 101 with only 100 shares. Is fair value the mid, 100.5? If not, where is it, and why?

Accepted Answer

The mid ignores the imbalance. The simple mid (100 + 101)/2 = 100.5 treats both sides symmetrically, but the book is wildly lopsided: 900 buyers waiting versus only 100 shares offered. The thin ask is far more likely to get consumed and lift than the deep bid is to be exhausted. Fair value is skewed toward the ask. The microprice. Weight each price by the size on the opposite side (equivalently, by the queue imbalance): P{	ext{micro}} = \frac{P{	ext{bid}}\,Q{	ext{ask}} + P{	ext{ask}}\,Q{	ext{bid}}}{Q{	ext{bid}} + Q{	ext{ask}}}. Plug in P{	ext{bid}} = 100,\ Q{	ext{bid}} = 900,\ P{	ex…

The microprice, when the mid lies

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