A Mathematical Framework for Modelling Order Book Dynamics#
2. Affiliation:#
Adrien De Larrard is affiliated with Université Paris-Dauphine, PSL
3. Keywords:#
Limit order book, stochastic model, quantitative finance, market microstructure, measure-valued process
4. Url:#
5. Summary:#
(1): The article presents a mathematic framework for modelling the dynamics of limit order books.
(2): Past methods include discretizing both time and price, leading to limitations in accurately representing market phenomena. The approach in this paper is well-motivated, as it provides a more flexible and accurate framework for modelling limit order books.
(3): The proposed methodology involves combining two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a deterministic ‘mass transport’ operator acting on distributions of buy and sell orders. The framework also includes a natural decomposition of the infinitesimal generator describing the evolution of the limit order book.
(4): The methods in this paper are applied to simulate and study the order book dynamics of various trading strategies, and results show that the framework provides more accurate insights into the interplay between order flow and price dynamics. The performance supports their goals of providing a more flexible and accurate framework for modelling limit order books.
6. Conclusion:#
(1): The significance of this piece of work lies in providing a more flexible and accurate mathematical framework for modelling limit order book dynamics in quantitative finance, especially in the field of market microstructure. The integration of general spatial point processes and deterministic mass transport operators provides a novel approach in studying the interplay between order flow and price dynamics.
(2): Innovation point: The proposed methodology in this article is innovative, as it combines two modelling ingredients that have not been integrated in previous studies of limit order book dynamics. The integration of order flow as a general spatial point process and deterministic mass transport operators in modelling market clearing provides a more accurate approach in describing phenomena in real markets.
(3): Performance: The methods in this paper have been applied to study order book dynamics for various trading strategies and have shown higher accuracy in describing the interplay between order flow and price dynamics. However, limitations in the computational efficiency of the methods may hinder broader applications in real-time applications.
(4): Workload: The paper includes a comprehensive presentation of the mathematical framework, with detailed derivation and explanation of the modelling ingredients. However, the level of mathematical sophistication may make the article less accessible to readers with less mathematical backgrounds.