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Price Impact

Definition

Price impact is the change in asset price caused by executing a trade or submitting orders to the market. A buy order pushes prices up; a sell order pushes them down. Price impact is a cost of trading and a central quantity in market microstructure.

Types

Type Description
Temporary impact Immediate price move from consuming liquidity; partially reverts after the trade
Permanent impact Lasting price change due to information content of the trade
Total impact Sum of temporary and permanent; the full cost to an execution algorithm

Empirical relationships

Linear OFI model (Cont, Kukanov & Stoikov 2010):

\[\Delta p_t = \beta \cdot \text{OFI}_t + \epsilon_t\]

where \(\beta \propto 1/\text{depth}\). This is the workhorse short-horizon model. See price-impact-order-book-events.

Square-root law (widely documented):

\[\Delta p \propto \sqrt{Q}\]

Price impact is concave in trade size \(Q\) — doubling the trade size does not double the price impact. Cont et al. derive this from the linear OFI model via a scaling argument.

Determinants

  • Market depth — deeper order books absorb flow more cheaply; \(\beta\) is smaller.
  • Volatility — higher volatility markets exhibit larger impact per unit of flow.
  • Trade size — impact grows sub-linearly (square-root law) with size.
  • Information content — informed trades have larger permanent impact.
  • Time of day — impact is typically higher near open/close when liquidity is thinner.

Relation to OFI

Short-horizon price impact is primarily driven by order-flow-imbalance, not by raw trade volume. The key insight from Cont et al. is that OFI — which measures the net pressure at the best bid/ask from all order book events (not just executed trades) — is a more robust predictor than volume alone.

Subsequent work has shown that aggregating across multiple book levels via integrated OFI raises OOS \(R^2\) from \(\sim\!65\%\) (best-level) to \(\sim\!84\%\) on Nasdaq-100 (cross-impact-ofi-equity-markets).

Cross-impact

In a multi-asset setting, price impact generalises to cross-impact — the effect of asset \(j\)'s order flow on asset \(i\)'s price. Empirically:

  • Contemporaneous cross-impact is negligible once you use integrated OFI (the multi-level aggregation subsumes it).
  • Predictive (lagged) cross-impact is real at short horizons (\(\leq 3\) min) and decays rapidly with forecast horizon.

Event-type decomposition

At the finest resolution, price impact can be decomposed by the six EBK event types — market orders, limit orders, and cancellations, each split into "at-best" and "inside-spread" variants. Key findings (eisler-bouchaud-kockelkoren-order-book-events, models-for-all-order-book-events):

  • Limit-order impact is real and ~60–70% of market-order impact — trade-tape-only studies underestimate total impact.
  • Large-tick stocks: bare impacts are permanent and non-fluctuating (simple constant-impact model fits).
  • Small-tick stocks: bare impacts acquire history dependence via gap fluctuations; a linear AR model on past event flow captures it.
  • The market-order-only propagator \(G(\tau)\) in earlier propagator work is "dressed" by unobserved LO/CA flow — separating them recovers the true bare impacts.

Open questions

  • What is the correct functional form of impact at large sizes? (Power law vs log?)
  • How does permanent vs temporary split vary by asset and market regime?
  • Do machine learning models add predictive power beyond linear OFI models?

Connections