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Ilya Dushin's avatar

Great breakdown, Annanay. You hit the nail on the head regarding the real challenge in microstructure modeling: while writing down a basic imbalance or decayed flow metric is straightforward, the entire edge hinges on how you define the "horizon" and how you fuse static book depth with dynamic flow velocity.

Two thoughts that connect directly to what you described:

1. The "Horizon Trap" and Martingale Pricing. Choosing an arbitrary fixed time horizon (e.g., 500 milliseconds vs. 5 seconds) often creates an econometric trap. As you noted, a fixed horizon forces a tradeoff between chasing tick-level microstructure noise and losing predictive Sharpe over longer windows. One powerful way modern microstructure resolves this is to eliminate arbitrary time horizons altogether. Instead of forecasting price differences over a fixed time delta, the target is formulated as the asymptotic conditional expectation of the mid-price - the theoretical martingale fair price (or micro-price) where the asset will settle once the current queue imbalances clear.

2. Coupling Queue Depth with Flow Velocity. In your post, you rightly highlight both decayed trade flow and order book imbalance as primary signals. In reality, these two are not separate features - they are physically coupled. Resting queue imbalances represent static inventory, while decayed flow represents continuous velocity. Flow velocity is literally the drift that pushes the imbalance toward the edge of the book before a quote sweep occurs.

We recently published a working paper that tackles this exact problem: moving beyond classical discrete models (like Stoikov's discrete micro-price) by treating continuous imbalance and order flow velocity as a coupled continuous-state system.

By applying spectral resolvent operators, we show that you can solve for the continuous fair price adjustment in closed form. This eliminates arbitrary forecast horizons, avoids discrete grid binning, and evaluates in single-digit nanoseconds while cutting forward prediction error by over 30% compared to traditional static imbalance models.

If you are interested in the mathematical formulation and empirical results on Level-3 tick data, you can find the full paper here: https://papers.ssrn.com/abstract=7433960

Excellent article - looking forward to reading more of your research on flow dynamics.

Vittorio Manente's avatar

Excellent article! I tried to build it on IBKR, lot of work. Worth it.

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