Diffusive Limit of Hawkes Driven Order Book Dynamics With Liquidity Migration

Battle Count: 97

The paper provides a rigorous theoretical foundation for modeling limit order book dynamics with self-exciting order flow and liquidity migration. While directly relevant to market microstructure research, optimal execution, and market making strategies, it is purely theoretical with no empirical validation, no trading signals, and no backtesting. Its value lies in providing a mathematically consistent bridge between high-frequency event-based models and tractable diffusion descriptions, which could inform future quantitative trading model development. The Laplacian coupling for liquidity migration is a novel contribution that could improve order book simulation fidelity.

Implementation requires advanced knowledge of stochastic calculus, multivariate Hawkes processes, reflected SDEs, Skorokhod reflection, functional central limit theorems, and generator theory for Markov processes. Numerical simulation of the resulting reflected multi-dimensional SDE with discrete Laplacian coupling and state-dependent coefficients is non-trivial. Calibration would require estimation of the full Hawkes kernel matrix from event data. The theoretical framework is self-contained but demands significant mathematical sophistication to implement or extend.

The paper is entirely theoretical with complete mathematical derivations provided (microscopic generator, Taylor expansion, FCLT application, reflected SDE formulation). All assumptions are explicitly stated (Hawkes stability, Lipschitz baselines, moment bounds, boundary behavior). However, there is no code, no numerical implementation, and no empirical data to validate against. Reproducibility is limited to verifying the mathematical proofs independently.