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Institution: School of Economics and Finance / Software Engineering, Xi'an Jiaotong University

The Price Impact of Generalized Order Flow Imbalance

Authors: Yuhan Su, Zeyu Sun, Jiarong Li, Xianghui Yuan Year: 2021 arXiv: 2112.02947 Categories: q-fin.TR

Plain-language abstract

Standard OFI (from price-impact-order-book-events) assumes a fixed minimum tick size, which breaks down when stocks trade in non-minimum quotation units. This paper introduces a generalised construction that handles variable tick sizes, then applies a log-stationarisation step to produce log-GOFI (Generalised Stationarised OFI). On CSI 500 constituent stocks, log-GOFI dramatically outperforms the original OFI: out-of-sample \(R^2\) rises from ~35–43% to ~84–86% across three time scales.

Key contributions

  1. Generalised OFI construction — extends Cont et al.'s OFI to handle non-minimum quotation units, common in Chinese equity markets.
  2. log-GOFI — log-stationarised version of generalised OFI; combines stationarity with the generalised construction.
  3. Empirical validation on CSI 500 — 10 representative stocks at 30s, 1min, 5min scales; all show substantial improvement over vanilla OFI.
  4. Stability — log-GOFI's explanatory power is consistently strong across all three time scales, while OFI degrades at longer scales.

Motivation and method

Why standard OFI breaks on Chinese data

Chinese stock exchanges publish order-book snapshots every 3 seconds, not on every event. In a 3-second window the best bid/ask can jump by multiple ticks (e.g., \(2\delta\)) — several limit-arrival / cancel cycles happen before the next observation. Standard OFI assumes within-interval price moves of at most \(\delta\), so it misrepresents these multi-tick displacements.

GOFI construction

Instead of tracking the best-price position and its single-tick moves, GOFI tracks the value of queue sizes across all price levels that participated in the optimal-price movement:

\[\text{GOFI}_n = \sum_{i=1}^{W_n^b} q^{b,i}_n - \sum_{i=1}^{W_n^b} q^{b,i-1}_n \;-\; \sum_{i=1}^{W_n^a} q^{a,i}_n + \sum_{i=1}^{W_n^a} q^{a,i-1}_n\]

where \(W_n^{b/a}\) is the number of price levels the best bid/ask swept through in interval \(n\), and \(q^{b,i}_n\) is the queue size at the \(i\)-th level. This absorbs multi-tick moves cleanly.

log variants (from Wang et al. 2021) replace each raw \(q\) with \(\log q\) to reduce the heavy-tailed variance of queue sizes, giving log-OFI and log-GOFI.

Four variants compared

Variant Handles multi-tick moves? Log-stationarised?
OFI no no
log-OFI no yes
GOFI yes no
log-GOFI yes yes

Main results

Average \(R^2\) across 10 CSI 500 stocks, out-of-sample linear regression of mid-price change on each indicator:

Indicator \(R^2\) (30s) \(R^2\) (1min) \(R^2\) (5min)
OFI (Cont et al.) 32.89% 38.13% 42.57%
log-OFI 40.35% 46.27% 51.65%
GOFI 76.37% 77.85% 77.36%
log-GOFI 83.57% 85.37% 86.01%

Two effects stack: - The generalisation (GOFI vs OFI) is the big lift on 3-second Chinese data — going from ~35% to ~77% R² by properly handling multi-tick moves. - The log stationarisation adds a further ~8 percentage points on top. - log-GOFI is also the most stable across time scales: 83 → 86% as horizon grows from 30s to 5min, whereas OFI degrades at shorter horizons where multi-tick moves dominate.

Limitations

  • Data is from Chinese equity markets (CSI 500) only; generalisation to other exchanges is unverified.
  • Evaluation uses linear regression only; non-linear models may perform differently relative to the baseline.
  • The paper focuses on a small sample of 10 stocks; broader validation would strengthen the claim.

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