Quantitative Calibration to Reproduce the Full Signature Plot, Including Short-Term Dynamics

Determine a quantitative calibration of the parameters of the generalized propagator and metaorder process that reproduces the full structure of the signature plot of the simulated price process, including short-term dynamics and not only the long-term diffusive behavior.

Background

The signature plot (variance per unit time versus aggregation scale) is a standard diagnostic of market microstructure, reflecting short-term trending or mean-reversion and long-term diffusion. The paper shows that diffusivity can be restored through metaorder sign correlations or volume-dependent impact decay.

The authors state that a full quantitative match to empirical signature plots, including short-term behavior, requires dedicated calibration of the model’s parameters. This constitutes an open task beyond the long-term diffusive results already demonstrated.