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

Battle Count: 53

Highly relevant to quantitative trading. The paper provides a rigorous framework for pathwise market impact estimation, which is central to execution cost analysis, optimal execution strategy design, and post-trade evaluation. The exact conditional simulation approach avoids the common pitfall of independent resampling that mixes execution effects with unrelated market noise. Applications include algorithmic execution, implementation shortfall analysis, and A/B testing of trading strategies. The event-driven algorithm is computationally efficient and parallelizable.

The theoretical framework requires strong background in point process theory, Poisson random measures, and stochastic calculus. The event-driven simulation algorithm (Algorithm 1) is implementable but requires careful handling of multiple event types (limit, cancel, market orders), conditional thinning, and Poisson cloud sampling. The closed-form impact formula (Theorem 4.5) under affine assumptions simplifies computation significantly. The a posteriori reconstruction (Algorithm 2) adds another layer of complexity. Monte Carlo parallelization is straightforward but requires many replications for accurate conditional distribution estimation.

The paper provides explicit algorithms (Algorithm 1 and Algorithm 2), detailed parameter specifications for numerical experiments, and a GitHub repository (https://github.com/tosmeow/passive-impact.git) with code for reproducing numerical experiments. However, the real data application uses E-mini S&P 500 futures data from May 29, 2025, which may not be freely available. The theoretical framework is fully self-contained with proofs in appendices.