Propagator Model

The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility: A Unifying Framework ArXiv ID: 2506.07711 “View on arXiv” Authors: Guillaume Maitrier, Jean-Philippe Bouchaud Abstract In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous “square-root law” of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the linear impact of order imbalances? Can one entirely explain the volatility of prices as resulting from the flow of uninformed metaorders that mechanically impact them? We introduce a new theoretical framework to describe metaorders with different signs, sizes and durations, which all impact prices as a square-root of volume but with a subsequent time decay. We show that, as in the original propagator model, price diffusion is ensured by the long memory of cross-correlations between metaorders. In order to account for the effect of strongly fluctuating volumes q of individual trades, we further introduce two q-dependent exponents, which allow us to describe how the moments of generalized volume imbalance and the correlation between price changes and generalized order flow imbalance scale with T. We predict in particular that the corresponding power-laws depend in a non-monotonic fashion on a parameter a, which allows one to put the same weight on all child orders or to overweight large ones, a behaviour that is clearly borne out by empirical data. We also predict that the correlation between price changes and volume imbalances should display a maximum as a function of a, which again matches observations. Such noteworthy agreement between theory and data suggests that our framework correctly captures the basic mechanism at the heart of price formation, namely the average impact of metaorders. We argue that our results support the “Order-Driven” theory of excess volatility, and are at odds with the idea that a “Fundamental” component accounts for a large share of the volatility of financial markets. ...

An Offline Learning Approach to Propagator Models ArXiv ID: 2309.02994 “View on arXiv” Authors: Unknown Abstract We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the propagator from a dataset containing correlated price trajectories, trading signals and metaorders. We quantify the accuracy of the estimated propagator using a metric which depends explicitly on the dataset. We show that a trader who tries to minimise her execution costs by using a greedy strategy purely based on the estimated propagator will encounter suboptimality due to so-called spurious correlation between the trading strategy and the estimator and due to intrinsic uncertainty resulting from a biased cost functional. By adopting an offline reinforcement learning approach, we introduce a pessimistic loss functional taking the uncertainty of the estimated propagator into account, with an optimiser which eliminates the spurious correlation, and derive an asymptotically optimal bound on the execution costs even without precise information on the true propagator. Numerical experiments are included to demonstrate the effectiveness of the proposed propagator estimator and the pessimistic trading strategy. ...