Exact Analytical Impact of Proxy Metaorders in the Generalized Propagator Model

Derive an exact analytical calculation of the price impact of proxy (synthetic) metaorders within the generalized propagator framework defined by G_q(t'→t) and the metaorder generation process described in the paper, so that the impact of these reconstructed metaorders can be computed analytically rather than solely via numerical simulation.

Background

The paper proposes a generalized propagator model that reproduces key stylized facts of market impact and price dynamics. It also introduces a procedure to construct proxy metaorders from trade-by-trade data, which empirically recovers the square-root law of market impact without trader identifiers.

While the simulator reproduces the square-root law and related statistics using proxy metaorders, the authors note that they do not yet have a closed-form analytical expression for the impact of such proxies within their model. Establishing this analytically would clarify when and why proxy metaorders match the impact of real metaorders and would provide a stronger theoretical foundation for the empirical procedures validated numerically.