L2 order book imbalance

Order book imbalance is arguably the single most validated short-term predictive signal in the market microstructure literature. The intuition is immediate: if there's substantially more resting size on the bid than the ask, the next price move is more likely upward.

The Cont-Kukanov-Stoikov framework

Cont, Kukanov & Stoikov (2014) provided the definitive empirical analysis, showing that order book imbalance — defined as:

$OBI = \frac{Q_{bid} - Q_{ask}}{Q_{bid} + Q_{ask}}$

predicts the direction of the next mid-price change with statistically and economically significant accuracy across multiple equity markets. The signal is monotonic: stronger imbalance produces larger expected price moves, and the relationship is approximately linear.

Their insight was that the imbalance captures the queue dynamics of the limit order book: when one side has substantially more depth, the probability that the opposite side is depleted first (triggering a price change toward the deeper side) increases mechanically.

Instantaneous vs. time-averaged

A single snapshot of imbalance is noisy — market makers continuously refresh quotes, and a momentary asymmetry can be an artifact of staggered updates. Huang & Polak (2011) showed that time-averaged imbalance over longer windows provides a smoother, more predictive signal that captures the sustained directional tilt of the book rather than transient fluctuations.

We compute both:

• Last imbalance — the snapshot at interval close
• Average imbalance — the mean imbalance across all quote updates in the interval

The divergence between them — how much the closing snapshot differs from the average — itself carries information. A large divergence indicates recent quote instability, suggesting a potential regime change within the bar.

L1 vs. L2: depth matters

Top-of-book (L1) imbalance captures only the best bid and ask. But Cao, Chen & Griffin (2005) demonstrated that information about future price changes exists at deeper levels of the book. A thin top-of-book bid sitting in front of massive size at deeper levels is structurally different from a thin bid with nothing behind it.

We compute L2 imbalance at cumulative depth tiers: 5, 10, 20, and 25 price levels per side. This captures the full shape of supply-demand imbalance, not just the frontier.

The L1-L2 divergence is the most actionable signal. When L1 shows thin bids but L2 reveals deep bid-side support, the apparent weakness is a mirage — the top-of-book thinness is likely a market maker adjusting inventory, not a genuine absence of demand. Conversely, thick L1 bids with empty L2 behind them indicate a single concentrated quote — remove that one market maker and there's a price gap.

References:

• Cont, R., Kukanov, A. & Stoikov, S. (2014). "The Price Impact of Order Book Events." Journal of Financial Econometrics, 12(1), 47–88.
• Huang, R. & Polak, T. (2011). "Lobster: Limit Order Book Reconstruction System." Working Paper, Humboldt-Universität zu Berlin.
• Cao, C., Chen, Z. & Griffin, J.M. (2005). "Informational Content of Option Volume Prior to Takeovers." Journal of Business, 78(3), 1073–1109.