Microprice with a two-cent tick

Question

The top of book shows: bid 10.00 with 4000 shares resting, ask 10.02 with 1000 shares. The tick here is two cents, so the spread spans 10.00 to 10.02. Where is fair value, and what does the book imbalance predict about the next tick?

Accepted Answer

The naive mid is (10.00 + 10.02)/2 = 10.01. It ignores that 4000 shares are stacked on the bid versus only 1000 offered, a heavily buy-leaning book. The microprice weights each price by the opposite side's queue: P{	ext{micro}} = \frac{P{	ext{bid}}\,Q{	ext{ask}} + P{	ext{ask}}\,Q{	ext{bid}}}{Q{	ext{bid}} + Q{	ext{ask}}} = \frac{10.00 \cdot 1000 + 10.02 \cdot 4000}{4000 + 1000}. Compute the numerator: 10{,}000 + 40{,}080 = 50{,}080, divided by 5000: P{	ext{micro}} = \frac{50{,}080}{5000} = 10.016. Fair value is about 10.016, not 10.01, pulled 80\% of the way to the ask. As an imbalance…

Microprice with a two-cent tick

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