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microstructural_features

Concept Overview

Features computed from bar-level order flow rather than from price alone, in three families: effective-spread proxies (Roll, Corwin-Schultz), price-impact coefficients (Kyle’s lambda, Amihud, Hasbrouck) and flow-toxicity or entropy measures (VPIN, plus Shannon, Lempel-Ziv and plug-in entropy over encoded tick signs). Together they estimate what OHLC bars omit: how expensive the instrument is to trade, and how likely it is that the counterparty knows something you do not.

When to Use

Use them as features when the edge or its cost depends on liquidity — execution models, regime detection, and any signal that decays with trade size. VPIN in particular is an early-warning indicator for flow toxicity ahead of liquidity events. Normalise within venue and time bucket before comparing across assets, since these are strongly regime-dependent, and freeze the symbol encoding used for entropy features or the values will not be comparable between training and production.

Mathematical Foundations

Kyle / Amihud / Hasbrouck Impact Families

$\Delta p_t=\lambda_K q_t+\epsilon_t,\qquad r_t=\lambda_A\frac{1}{DV_t}+\epsilon_t,\qquad r_t=\lambda_H\frac{q_t}{\sqrt{DV_t}}+\epsilon_t$

Spread and Volatility Proxies

$\text{Roll spread}\approx 2\sqrt{-\operatorname{cov}(\Delta p_t,\Delta p_{t-1})},\qquad\sigma_{CS}=f(H_t,L_t,H_{t-1},L_{t-1})$

Flow Toxicity and Entropy

$\mathrm{VPIN}_t=\frac{1}{V_t}\cdot\frac{1}{n}\sum_{i=t-n+1}^{t}\left|V_i^{B}-V_i^{S}\right|,\qquad H=-\sum_j p_j\log p_j$

where $V_i^{B}$ and $V_i^{S}$ are buy- and sell-initiated volume in bar $i$ (get_bvc_buy_volume will estimate the split when it is not observed), $V_t$ the current bar’s total volume, and $n$ the rolling window. The normaliser sits outside the sum because bars are not equal-volume: get_vpin averages the imbalance over the window and then scales by the latest bar. The equal-volume-bucket form used by streaming-hpc divides each term by the same constant bucket size instead; the two agree when bars carry equal volume. $H$ is the entropy of the tick-sign message, with $p_j$ the empirical frequency of symbol $j$ .

Usage Examples

Rust

End-to-end: Build Core Liquidity Feature Panel

use openquant::microstructural_features::{
    get_roll_measure,
    get_corwin_schultz_estimator,
    get_bar_based_kyle_lambda,
    get_bar_based_amihud_lambda,
    get_vpin,
};

// 1) Inputs from bar construction
let close = vec![100.0, 100.2, 100.1, 100.3, 100.25, 100.4];
let high = vec![100.1, 100.25, 100.2, 100.35, 100.3, 100.45];
let low = vec![99.9, 100.0, 99.95, 100.1, 100.05, 100.2];
let volume = vec![1000.0, 1200.0, 900.0, 1100.0, 1300.0, 1250.0];
let dollar_volume: Vec<f64> = close.iter().zip(volume.iter()).map(|(p, v)| p * v).collect();
let buy_volume = vec![600.0, 700.0, 480.0, 650.0, 800.0, 760.0];

// 2) Liquidity and spread proxies
let roll = get_roll_measure(&close, 3);
let cs_spread = get_corwin_schultz_estimator(&high, &low, 3);
let kyle = get_bar_based_kyle_lambda(&close, &volume, 3);
let amihud = get_bar_based_amihud_lambda(&close, &dollar_volume, 3);
let vpin = get_vpin(&volume, &buy_volume, 3);

// 3) Feature panel is ready for regime model / execution model
assert_eq!(roll.len(), close.len());
assert_eq!(vpin.len(), close.len());

From Encoded Tick Signs to Entropy Features

use openquant::microstructural_features::{
    encode_tick_rule_array,
    get_shannon_entropy,
    get_lempel_ziv_entropy,
    get_plug_in_entropy,
};

let tick_rule = vec![1, 1, -1, -1, 1, -1, 1, 1, 1, -1];
let msg = encode_tick_rule_array(&tick_rule)?;

let h_shannon = get_shannon_entropy(&msg);
let h_lz = get_lempel_ziv_entropy(&msg);
let h_plugin = get_plug_in_entropy(&msg, 2);

assert!(h_shannon.is_finite());
assert!(h_lz.is_finite());
assert!(h_plugin.is_finite());

API Reference

Python API

microstructural.get_roll_measure
microstructural.get_roll_impact
microstructural.get_corwin_schultz_estimator
microstructural.get_bekker_parkinson_vol
microstructural.get_bar_based_kyle_lambda
microstructural.get_bar_based_amihud_lambda
microstructural.get_bar_based_hasbrouck_lambda
microstructural.get_trades_based_kyle_lambda
microstructural.get_trades_based_amihud_lambda
microstructural.get_trades_based_hasbrouck_lambda
microstructural.vwap
microstructural.get_avg_tick_size
microstructural.get_vpin
microstructural.get_bvc_buy_volume
microstructural.encode_tick_rule_array
microstructural.quantile_mapping
microstructural.sigma_mapping
microstructural.encode_array
microstructural.get_shannon_entropy
microstructural.get_lempel_ziv_entropy
microstructural.get_plug_in_entropy
microstructural.get_konto_entropy

Rust API

get_roll_measure
get_corwin_schultz_estimator
get_bar_based_kyle_lambda
get_vpin
MicrostructuralFeaturesGenerator

Risk Notes and Caveats

Microstructure signals are highly regime-dependent; normalize and standardize within venue/time bucket before cross-asset comparison.
Use shared bar definitions between training and live pipelines, otherwise feature drift is structural.
Entropy features are sensitive to encoding; freeze symbol maps in production.