We revisit the classical problem of market impact through the lens of a new agent-based model. Drawing from the mean-field approach in Statistical Mechanics and Physics, we assume a large number of agents interacting in the order book . By taking the 'continuum' limit we obtain a set of nonlinear differential equations, the core of our dynamical theory of price formation. And we explicitly solve them using Fourier analysis. One could talk as well of a "micro-macro" approach of equilibrium, where the market price is the consequence of each ("microscopic") agent behaving with respect to his preferences and to global ("macroscopic") information. When a large market order (or metaorder) perturbs the market, our model recovers the square-root law of impact , providing new insights on the price formation process. In addition, we give various limiting cases, examples and possible extensions .
The latent order book of Donier et al. is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book .
R
We revisit the classical problem of market impact through the lens of a new
The latent order book of Donier et al. is one of the most promising
R
model. Drawing from the
models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a
R
approach in Statistical Mechanics and Physics, we assume a large number of agents interacting in the order book . By taking the 'continuum' limit we obtain a set of nonlinear differential equations, the core of our dynamical theory of price formation. And we explicitly solve them using Fourier analysis. One could talk as well of a "micro-macro" approach of equilibrium, where the market price is the consequence of each ("microscopic") agent behaving with respect to his preferences and to global ("macroscopic") information. When a large market order (or metaorder) perturbs the market, our model recovers the square-root law of impact , providing new insights on the price formation process. In addition, we give various limiting cases, examples and possible extensions
assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book