Exact conditional simulation of Point processes: Application to pathwise market impact estimation

2026-07-03

AI Summary

Estimating market impact requires reconstructing counterfactual price paths for unexecuted trades under shared sources of randomness, yet these paths are inherently unobservable. This work proposes the first exact conditional simulation method for history-dependent marked point processes, leveraging a sparse representation of Poisson random measures to enable event-driven reconstruction of counterfactual trajectories under perturbed intensities. The approach yields unbiased and consistent path-level estimates of market impact for aggressive, passive, and hybrid trading strategies alike, establishing a rigorous theoretical foundation and an efficient computational framework for evaluating trading impact in high-frequency settings.

Abstract

Market impact is defined as the difference between the observed price trajectory under a given execution strategy and the counterfactual trajectory that would have prevailed without it. Since this counterfactual is unobservable, estimating market impact requires simulating alternative paths under the same realized market randomness. We address this by studying the conditional simulation of point processes under perturbed intensities. Given an observed counting process whose intensity is determined by its own history, we characterize the conditional law of the latent Poisson random measure in a thinning representation. This yields an exact, event-driven algorithm that reconstructs counterfactual paths on a common randomness source, enabling rigorous pathwise market impact estimation for aggressive, passive, and mixed strategies.

Problem

• market impact
• counterfactual estimation
• point processes
• conditional simulation
• pathwise analysis

Innovation

• exact conditional simulation
• point processes
• market impact estimation
• Poisson random measure
• event-driven algorithm