Easley / López de Prado VPIN

Authoritative reference

Easley, D., López de Prado, M. M. & O'Hara, M. (2012). Flow Toxicity and Liquidity in a High-Frequency World. Review of Financial Studies 25(5), 1457–1493.

DOI: https://doi.org/10.1093/rfs/hhs053.

OUP abstract: https://academic.oup.com/rfs/article/25/5/1457/1574328.

Consumed by

Vpin — the engine's order-flow toxicity analytic.

Algorithm

1. Volume buckets. Slice the trade stream into equal-volume buckets of size V_bucket (default 10 000 shares).
2. Side classification per bucket. Each trade's volume splits into buy-volume and sell-volume per the configured classifier:
   • Tick rule. Verbatim per the 2012 paper.
   • BVC with EWMA-smoothed σ_ΔP. Bulk-Volume Classification using an EWMA estimate of the per-trade price-change standard deviation, with $\alpha$ default 0.10.
3. Sliding-window VPIN. Over the most recent $n$ completed buckets, the published ELO 2012 form is:

$${\mathit{\text{VPIN}}}_{\text{ELO}}=\frac{1}{n}\sum _{k=1}^n\frac{|V_k^{\text{buy}}-V_k^{\text{sell}}|}{V^{\text{bucket}}}$$

where $V^{\text{bucket}}$ is the configured bucket-volume target.

Implementation deviation from ELO 2012

The crate divides by the per-bucket actual closed volume $V_k^{\text{total}}$ rather than the configured target $V^{\text{bucket}}$:

$${\mathit{\text{VPIN}}}_{\text{engine}}=\frac{1}{n}\sum _{k=1}^n\frac{|V_k^{\text{buy}}-V_k^{\text{sell}}|}{V_k^{\text{total}}}$$

The two forms agree exactly when every bucket fills exactly on a trade boundary (the ELO 2012 idealisation). They differ when proportional spillover (next section) causes $V_k^{\text{total}}$ to overshoot $V^{\text{bucket}}$ by the spilled-over surplus. The per-term ratio sits in $[V^{\text{bucket}}/(V^{\text{bucket}}+s_{max}),1]$ where $s_{max}$ is the largest single trade size admitted across the bucket boundary; under typical equity-flow size distributions the term-level divergence stays well under 1 % of $V^{\text{bucket}}$.

Consumers who need exact reconciliation against an externally maintained ELO 2012 series should record $V_k^{\text{total}}$ from the crate's per-bucket emission and rescale on their side.

Spillover

When a trade's size overshoots the current bucket's remaining capacity, the surplus seeds the next bucket proportional to the trade's classifier-derived buy-fraction so the across-bucket aggregation matches the un-split aggregate.

Implementation deviation from ELO 2012

ELO 2012 does not specify a spillover rule. The crate ships proportional spillover — the conventional production implementation choice that avoids biasing VPIN downward in high-activity windows. The crate documents this deviation explicitly so consumers can reason about behaviour at session boundaries.

Warm-up

VpinParams::warmup_buckets (default 30) suppresses emissions until the sliding window is at least that many buckets full. The first emission carries bucket_count >= warmup_buckets.

Validation

VpinParams::validate rejects window_size = 0, bucket_volume = 0, and BvcWithEwmaSigma { alpha } outside (0, 1] at construction time — a misconfigured spec surfaces VpinSpecError instead of silently degrading.