Market Impact Estimation via Causal Foundation Models

Dennis Thumm; Ying Chen

cs.LGOct 8, 2026

Market Impact Estimation via Causal Foundation Models

Authors: Dennis Thumm, Ying Chen

Organizations: National University of Singapore Singapore, Singapore

Abstract

When a trader executes a large order, the relevant question is not what will the price be? but what would the price have been had I not traded? Market impact is thus a causal quantity, yet classical models (Almgren--Chriss, propagators) regress price on flow, which is biased whenever informed flow moves prices through information as well as trading. We present a proof-of-concept Causal Market Simulator: a continuous-time causal prior-data fitted network (PFN) trained on a synthetic market prior in which a hidden informational flow confounds the flow--price relation by construction, with confounding strength an exact per-episode knob. On this prior, the naive estimator's bias follows a closed form we confirm empirically (up to 68% overestimation), while the PFN tracks the unbiased true-parameter oracle at high confounding. Its do-ablated twin, the same model with the intervention inputs removed, collapses onto the pre-window mean. Zero-shot, the model responds at the ground-truth scale to metaorders in an ABIDES limit-order book ( $+0.38$ pre-onset standard deviations against seed-replay counterfactuals), and its intervention response replicates on about 2,300 detected flow bursts in BTC/ETH/SOL perpetuals and 3,800 on Nasdaq equities, evidence consistent with, though not proof of, causal transfer. Off-prior the response degrades gracefully, and split-conformal recalibration repairs interval calibration. Transfer hinges on encoding the metaorder as added flow rather than a clamped price level, not on more training. A recurrent state-space variant closes the remaining shape gap: its impact accrues over execution duration where the transformer's stays flat, raising the correlation with measured metaorder impact from $+0.68$ to between $+0.92$ and $+0.96$ , at the cost of weaker on-prior deconfounding that traces to the training recipe rather than to recurrence.

Figures & tables

Panel of Figure 1 — Figure 1. The transformer instantiation ( $X(t_{i})$ : observable variables; core $U$ hidden): intervention specification and query enter a cross-variable mixer whose quantile head emits the interventional distribution. The do-ablated twin zeroes the dashed block and nothing else. The recurrent variant (below) replaces the encoder and mixer with $\Delta t_{i}$ -gated recurrences that inject the intervention at each active step. Block diagram of the transformer instantiation. Pre-intervention context tokens enter a temporal encoder with Fourier time features. The intervention specification (target, kind, value, window) and the query (outcome variable and time) enter a cross-variable mixer, and a quantile head outputs the interventional distribution of the queried outcome. The intervention block is dashed to mark the inputs that the do-ablated twin zeroes.

Figure 2. Synthetic proof of concept (transformer pair, native prior units). Left: the confounding law, measured. Naive observational OLS slope (blue) and interventional slope (green) vs. informational coupling

\gamma

; dashed lines are the closed forms (measured

\gamma

-gradient

0.326

vs.

0.332

analytic, Eq. ( 6 )); core share

s{=}0.7

; per-point SEs

\leq 0.011

\leq 0.023

(

n{=}2000

200

). Right: methods on the confounded market (

n{=}500

episodes per

\gamma

, identical across methods; bands are episode-bootstrap 95% CIs). Signed bias in the impact direction, and RMSE against the exact counterfactual. Left: line chart of the estimated impact slope against the informational coupling gamma from 0 to 2. The naive observational slope rises linearly from about 0.33 to about 0.98 while the interventional slope stays flat near 0.59; dashed lines show the analytic closed forms, which the measured curves track. Right: two line charts against gamma with shaded bootstrap bands, signed bias and RMSE. Almgren-Chriss bias rises linearly to about 1.7, the causal M-DoT-PFN stays within 0.25 of the unbiased parameter oracle at zero, the do-ablated twin coincides with the pre-window mean near minus 0.75, and the causal M-DoT-PFN's RMSE stays below the classical baselines for gamma at or above 1.

Table 3

Quantitative Finance

Quantitative finance uses mathematical models, statistics, and machine learning to value assets, measure risk, and guide trading and portfolio decisions.

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Abstract

Quantitative Finance

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