Market microstructure#

Order flow and liquidity from trades and quotes: trade signing, imbalance, price impact, and arrival intensity.

Trade signing#

Classify each trade as buyer- or seller-initiated to recover signed order flow.

Function	Description
Bulk Volume Classifier (BVC)	Buy-initiated share of a bar's volume estimated as the normal CDF of return / trailing-window volatility.
Lee-Ready Trade Sign	Trade sign by the Lee-Ready (1991) rule: quote test with tick-rule fallback.
Signed Volume	Aggressor-signed volume, sign * volume.
Tick Rule Sign	Trade sign by the tick rule (+1 up-tick, -1 down-tick, carry on unchanged).

Net buying pressure and its toxicity: trade-flow imbalance, book imbalance, and VPIN.

Function	Description
Cont Order-Flow Imbalance (order book)	Cont-Kukanov-Stoikov (2014) order-flow imbalance from L1 book events.
Order-Flow Imbalance	Normalized signed order flow, (buy - sell) / (buy + sell).
Queue (Book) Imbalance	Normalized L1 book imbalance, (bid_size - ask_size) / (bid_size + ask_size).
Rolling Order Imbalance	Trailing-window sum of signed order flow (Chordia-Roll-Subrahmanyam imbalance).
VPIN Order-Flow Toxicity	Volume-synchronized probability of informed trading (Easley-Lopez de Prado-O'Hara 2012): order-flow toxicity.

How far order flow moves price and what trading costs: Kyle's lambda, Amihud, Roll spread, the propagator, and the micro-price.

Function	Description
Amihud Illiquidity	Rolling mean of \|return\| / notional (Amihud 2002 illiquidity ratio).
Effective Spread	Effective spread, 2*\|price - mid\|: the round-trip cost paid relative to the mid.
Kyle's Lambda (exponentially weighted)	Exponentially-weighted price-impact slope of return on signed order flow.
Micro-Price (imbalance-weighted mid)	Imbalance-weighted mid (Stoikov 2018, first-order): fair value that leans toward the thinner side of the book.
Bouchaud Propagator Price Impact	Bouchaud (2004) propagator model: price impact as a decaying-kernel convolution over past signed order flow.
Realized Spread	Realized spread, 2D(price - mid a few steps later): the liquidity part of the effective spread.
Kyle's Lambda (rolling)	Rolling-window price-impact slope of return on signed order flow (Kyle 1985).
Roll Effective Spread	Roll (1984) effective spread from trade prices alone: 2*sqrt(-cov(dP_t, dP_{t-1})) over a trailing window.

The timing and clustering of trades: self-exciting arrival intensity.

Function	Description
Hawkes Process Conditional Intensity	Conditional intensity of an exponential-kernel Hawkes process: lambda_t = mu + kappa_t.