Parameter Calibration

This tab demonstrates how η and γ would be estimated from execution data using heteroskedastic weighted least squares, following Almgren (2005) §4. Synthetic fills are generated from the model itself — with η = 0.142, γ = 0.314 (Almgren 2005, Table 3) as the known ground truth — so recovery accuracy can be verified directly. The fills, noise model, and regression are implemented verbatim from the verify_calibration.py harness in the project root.

The noise model scales measurement error as a fraction of the price-path diffusion σ·√(T/6.5), calibrated so that at N = 5,000 orders the standard errors match the Almgren 2005 Table 3 benchmarks: SE(γ̂)/γ ≈ 13% and SE(η̂)/η ≈ 4%. Standard errors reflect single-realisation uncertainty; seed variation is small and unbiased — the estimator is consistent. With real execution data the procedure would be identical, but η̂ and γ̂ would reflect actual market conditions rather than recovering a known ground truth.

The three plots below mirror Almgren (2005) Figure 4: calibration scatter with fitted line, parameter recovery bar chart with ±1 SE error bars, and residual Q-Q plots against N(0,1). Well-specified residuals should hug the diagonal — systematic departures indicate model mis-specification.