Liquidity Modeling

DiffVolume: Diffusion Models for Volume Generation in Limit Order Books ArXiv ID: 2508.08698 “View on arXiv” Authors: Zhuohan Wang, Carmine Ventre Abstract Modeling limit order books (LOBs) dynamics is a fundamental problem in market microstructure research. In particular, generating high-dimensional volume snapshots with strong temporal and liquidity-dependent patterns remains a challenging task, despite recent work exploring the application of Generative Adversarial Networks to LOBs. In this work, we propose a conditional \textbf{“Diff”}usion model for the generation of future LOB \textbf{“Volume”} snapshots (\textbf{“DiffVolume”}). We evaluate our model across three axes: (1) \textit{“Realism”}, where we show that DiffVolume, conditioned on past volume history and time of day, better reproduces statistical properties such as marginal distribution, spatial correlation, and autocorrelation decay; (2) \textit{“Counterfactual generation”}, allowing for controllable generation under hypothetical liquidity scenarios by additionally conditioning on a target future liquidity profile; and (3) \textit{“Downstream prediction”}, where we show that the synthetic counterfactual data from our model improves the performance of future liquidity forecasting models. Together, these results suggest that DiffVolume provides a powerful and flexible framework for realistic and controllable LOB volume generation. ...

Non cooperative Liquidity Games and their application to bond market trading ArXiv ID: 2405.02865 “View on arXiv” Authors: Unknown Abstract We present a new type of game, the Liquidity Game. We draw inspiration from the UK government bond market and apply game theoretic approaches to its analysis. In Liquidity Games, market participants (agents) use non-cooperative games where the players’ utility is directly defined by the liquidity of the game itself, offering a paradigm shift in our understanding of market dynamics. Each player’s utility is intricately linked to the liquidity generated within the game, making the utility endogenous and dynamic. Players are not just passive recipients of utility based on external factors but active participants whose strategies and actions collectively shape and are shaped by the liquidity of the market. This reflexivity introduces a level of complexity and realism previously unattainable in conventional models. We apply Liquidity Game theoretic approaches to a simple UK bond market interaction and present results for market design and strategic behavior of participants. We tackle one of the largest issues within this mechanism, namely what strategy should market makers utilize when uncertain about the type of market maker they are interacting with, and what structure might regulators wish to see. ...

Relative entropy-regularized robust optimal order execution ArXiv ID: 2311.06476 “View on arXiv” Authors: Unknown Abstract The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent’s goal is to maximize an objective functional associated with his profit-and-loss of trading and simultaneously minimize the execution risk and the market’s liquidity and uncertainty. We model the market’s liquidity and uncertainty by the principle of least relative entropy associated with the market volume. The problem of order execution is made into a relative entropy-regularized stochastic differential game. Standard argument of dynamic programming yields that the value function of the differential game satisfies a relative entropy-regularized Hamilton-Jacobi-Isaacs (rHJI) equation. Under the assumptions of linear-quadratic model with Gaussian prior, the rHJI equation reduces to a system of Riccati and linear differential equations. Further imposing constancy of the corresponding coefficients, the system of differential equations can be solved in closed form, resulting in analytical expressions for optimal strategy and trajectory as well as the posterior distribution of market volume. Numerical examples illustrating the optimal strategies and the comparisons with conventional trading strategies are conducted. ...

Uncovering Market Disorder and Liquidity Trends Detection ArXiv ID: 2310.09273 “View on arXiv” Authors: Unknown Abstract The primary objective of this paper is to conceive and develop a new methodology to detect notable changes in liquidity within an order-driven market. We study a market liquidity model which allows us to dynamically quantify the level of liquidity of a traded asset using its limit order book data. The proposed metric holds potential for enhancing the aggressiveness of optimal execution algorithms, minimizing market impact and transaction costs, and serving as a reliable indicator of market liquidity for market makers. As part of our approach, we employ Marked Hawkes processes to model trades-through which constitute our liquidity proxy. Subsequently, our focus lies in accurately identifying the moment when a significant increase or decrease in its intensity takes place. We consider the minimax quickest detection problem of unobservable changes in the intensity of a doubly-stochastic Poisson process. The goal is to develop a stopping rule that minimizes the robust Lorden criterion, measured in terms of the number of events until detection, for both worst-case delay and false alarm constraint. We prove our procedure’s optimality in the case of a Cox process with simultaneous jumps, while considering a finite time horizon. Finally, this novel approach is empirically validated by means of real market data analyses. ...