Optimal Trading of Microstructure Mean Reversion

Battle Count: 89

Directly addresses optimal trading of microstructure mean reversion at the seconds timescale. Provides closed-form formulas for optimal band width and profit rate. The result that 'all profit is the option value of waiting' and the myopic rule earning zero are practically significant. The one-number characterization (gamma = phi/s_G) simplifies strategy calibration. Highly relevant for HFT firms trading liquid large-tick assets.

The final formulas are simple closed-form: theta*(theta*-phi) = s_G^2 and R* = alpha*s_G*sqrt(2/pi)*exp(-u*^2/2). However, implementation requires: (1) estimating the gap autocovariance to identify (alpha, s_G), (2) filtering the latent efficient price from observable quotes, (3) monitoring the parity state of the mid, (4) executing at the touch with correct spread accounting. The theoretical model is complex but the trading rule itself is a simple two-threshold band.

The paper is fully theoretical with complete proofs in appendices. All formulas are closed-form. However, no code repository is provided, parameters are illustrative (not calibrated to real data), and the Monte Carlo simulations in Section 3.1 lack published code. The model requires estimation of (alpha, s_G) from gap autocovariance, which is described but not demonstrated on real data.