Anomalous diffusion and price impact in the fluid-limit of an order book
arXiv:2310.06079 · doi:10.1016/j.cam.2024.116202
Abstract
We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic forcing function with non-uniformly sampled times between order book events in the setting of fractional diffusion. This models the fluid limit of an order book by modelling the continuous arrival, cancellation and diffusion of orders in the presence of information shocks. We study the impulse response and stylised facts of orders undergoing anomalous diffusion for different forcing functions and model parameters. Concretely, we demonstrate the price impact for flash limit-orders and market orders and show how the numerical method generate kinks in the price impact. We use cubic spline interpolation to generate smoothed price impact curves. The work promotes the use of non-uniform sampling in the presence of diffusive dynamics as the preferred simulation method.
arXiv comment36 pages, 23 figures, 4 tables; Accepted, Journal of Computational and Applied Mathematics. Clarified notation and added additional commentary and interpretation of this model
References in corpus (11)
- Price Variations in a Stock Market With Many Agents
- Statistical theory of the continuous double auction
- The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows
- Anomalous price impact and the critical nature of liquidity in financial markets
- Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
- Anomalous impact in reaction-diffusion models
- Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders
- Reaction-Diffusion-Branching Models of Stock Price Fluctuations
- Kinetic Theory for Finance Brownian Motion from Microscopic Dynamics
- Deviations in expected price impact for small transaction volumes under fee restructuring
- The Epps effect under alternative sampling schemes