Why is the estimation of metaorder impact with public market data so challenging?

TL;DR

The paper examines why estimating metaorder impact from public market data yields price trajectories that differ markedly from real executions. It systematically compares linear (Hasbrouck TIM) and nonlinear (CNN–LSTM) models calibrated on public data using a generalized IRF, finding that they tend to produce near-linear intra-execution growth with limited reversion, contrary to empirical concavity and convex reversion. To resolve this, the authors introduce a modified Transient Impact Model with a tunable parameter α that partitions a metaorder's influence between price formation and order flow, and show that near a critical regime this can reproduce the observed linear growth and partial memory, including possible permanent impact. The work ties the discrepancy to the interpretation of order-flow autocorrelation (LMF theory) and demonstrates the importance of how metaorder information is injected into volume versus price dynamics, offering a framework to better align public-data models with stylized facts and informing transaction-cost analyses. Practical implications include improved understanding of when public-data models may misprice impact costs and how to calibrate models to avoid spurious conclusions about long-term impact.

Abstract

Estimating market impact and transaction costs of large trades (metaorders) is a very important topic in finance. However, using models of price and trade based on public market data provide average price trajectories which are qualitatively different from what is observed during real metaorder executions: the price increases linearly, rather than in a concave way, during the execution and the amount of reversion after its end is very limited. We claim that this is a generic phenomenon due to the fact that even sophisticated statistical models are unable to correctly describe the origin of the autocorrelation of the order flow. We propose a modified Transient Impact Model which provides more realistic trajectories by assuming that only a fraction of the metaorder trading triggers market order flow. Interestingly, in our model there is a critical condition on the kernels of the price and order flow equations in which market impact becomes permanent.

Figures (14)

• Figure 1: The figure shows the two possible conventions that can be adopted to define the price variation at time $t$.
• Figure 2: Cumulative $d_i$ parameter plots with $p = 2 \times 10^{3}$ and $p = 4 \times 10^{3}$ for Amazon (left panel) and Microsoft (right panel).
• Figure 3: Simulated price trajectory with respectively $p= 2 \times 10^{3}$ (left panel) and $p = 4 \times 10^{3}$ (right panel), for Amazon featuring metaorder execution for $T = 1000$.
• Figure 4: Simulated price trajectory with respectively $p= 2 \times 10^{3}$ (left panel) and $p = 4 \times 10^{3}$ (right panel), for Microsoft featuring metaorder execution for $T = 1000$.
• Figure 5: Price dynamics during and after the execution of a metaorder of length $T=50$ using a Neural Network calibrated on Microsoft data. The left panel shows the case of 5 lags while the right one the case of 100 lags. The right panel also shows an inertia effect which makes the price increase also after the end of the metaorder execution.

Theorems & Definitions (1)

• Remark