Related papers: Second order approximations for limit order books
We introduce a new approximate solution technique for first-order Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of first-order basis functions, we compute suitable weights by casting the…
We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…
We provide an explicit characterization of the optimal market making strategy in a discrete-time Limit Order Book (LOB). In our model, the number of filled orders during each period depends linearly on the distance between the fundamental…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past…
In order-driven markets, limit-order book (LOB) resiliency is an important microscopic indicator of market quality when the order book is hit by a liquidity shock and plays an essential role in the design of optimal submission strategies of…
The latent order book of \cite{donier2015fully} 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…
We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock…
We consider a simplified model of the continuous double auction where prices are integers varying from $1$ to $N$ with limit orders and market orders, but quantity per order limited to a single share. For this model, the order process is…
In this paper, we introduce a parametrized family of prices derived from the Maximum Entropy Principle. The price is obtained from the distribution that minimizes bias, given the bid and ask volume imbalance at the top of the order book.…
We conduct modeling of the price dynamics following order flow imbalance in market microstructure and apply the model to the analysis of Chinese CSI 300 Index Futures. There are three findings. The first is that the order flow imbalance is…
Robustness of the solutions to the inflaton potential inverse problem based on the slow-roll approximation is addressed. With that aim it is introduced a measure of the difference of the outputs obtained using first and second order…
This paper develops a model of liquidity provision in financial markets by adapting the Madhavan, Richardson, and Roomans (1997) price formation model to realistic order books with quote discretization and liquidity rebates. We postulate…
Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…
We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By…
This paper develops a theoretical mesoscopic model of the limit order book driven by multivariate Hawkes processes, designed to capture temporal self-excitation and the spatial propagation of order flow across price levels. In contrast to…
In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in…
We introduce a practical, interactive simulator of the limit order book for large-tick assets, designed to produce realistic execution, costs, and P&L. The book state is projected onto a tractable representation based on spread and volume…
The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale…
Order book dynamics play an important role in both execution time and price formation of orders in an exchange market. In this study, we aim to model the limit order arrival rates in the vicinity of the best bid and the best ask price…