Order Flow Imbalance (OFI)

Formula

Per-event contribution (Cont, Kukanov & Stoikov, 2014):

eₙ =  1{Pᴮₙ ≥ Pᴮₙ₋₁}·qᴮₙ − 1{Pᴮₙ ≤ Pᴮₙ₋₁}·qᴮₙ₋₁
    − 1{Pᴬₙ ≤ Pᴬₙ₋₁}·qᴬₙ + 1{Pᴬₙ ≥ Pᴬₙ₋₁}·qᴬₙ₋₁

OFIₖ = Σ eₙ   over events n in interval k

Price impact:  ΔPₖ ≈ βₖ · OFIₖ + εₖ,   βₖ ∝ 1 / average depth

Pᴮ, qᴮ : best bid price and size     Pᴬ, qᴬ : best ask price and size

Interpretation

• When the bid price is unchanged, the bid term reduces to the change in bid size. A rising bid counts the full new size, and a falling bid subtracts the full old size. The ask side mirrors this with the sign flipped.
• The original study on US equities reports that a single linear OFI regression explains a large share of short-interval mid-price variance. It also finds that the impact coefficient scales inversely with market depth.

Institutional usage

• Short-horizon alpha and quote-skewing signals for market makers.
• Execution: pausing or accelerating child orders when OFI runs against the order.
• Multi-level OFI, computed over the top N levels, adds information beyond level 1 in deeper books.

Pitfalls

• Snapshot data such as the 3-second L2 snapshots common in A-share feeds hides intermediate events, so OFI computed from snapshots is a coarse approximation.
• Normalise by average depth or volume before comparing OFI across stocks.

Python reference implementation

Requires numpy, pandas. Tested before publication; the generator re-executes it on every rebuild. MIT licensed. Download ofi.py · All snippets

import numpy as np
import pandas as pd

def ofi(book: pd.DataFrame) -> pd.Series:
    """Per-event order flow imbalance e_n (Cont, Kukanov & Stoikov, 2014).
    book: rows are successive top-of-book snapshots with columns
          bid_px, bid_sz, ask_px, ask_sz.
    Sum e_n over a time window to get OFI for that window."""
    bp, bq = book["bid_px"], book["bid_sz"]
    ap, aq = book["ask_px"], book["ask_sz"]
    bp0, bq0, ap0, aq0 = bp.shift(), bq.shift(), ap.shift(), aq.shift()
    e = (np.where(bp >= bp0, bq, 0.0) - np.where(bp <= bp0, bq0, 0.0)
         - np.where(ap <= ap0, aq, 0.0) + np.where(ap >= ap0, aq0, 0.0))
    e = pd.Series(e, index=book.index)
    e.iloc[0] = 0.0  # no previous snapshot
    return e

# Window OFI, e.g. 10-second buckets:
# ofi_10s = ofi(book).resample("10s").sum()

FAQ

Can OFI be computed from trade data alone?

No. OFI needs best bid/ask prices and sizes. Trade-only data gives trade-sign imbalance (buy volume minus sell volume), a related but different measure.