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 markets. This modification leads to new order book dynamics, which we explicitly study …
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A weak law of large numbers for a limit order book model with fully state dependent order dynamicsq-fin.MF
This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and the standing volume densities on both sides of the LOB we derive a weak law of …
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a…
Equity auctions show linear price impact up to a large volume, then non-linear.
problem Understanding price impact in equity auctions.
method High-quality data analysis of Paris stock exchange auctions.
result Price impact is linear up to a large volume, then becomes non-linear.
We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which …
The paper models financial order books using geometric shears and directional liquidity.
problem Understanding the geometry and dynamics of financial order books.
method Structural framework modeling liquidity as emergent observables, geometric shears, and directional imbalances.
result The geometry of financial order books can be described by a rigid drift and geometric shear, leading to a gamma-like profile of projected liquidity.
In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. [Phys. Rev. Lett. 120, 138301] and financial herd behavior model. Combining these approaches allows us to propose a mo…
In this paper we derive a scaling limit for an infinite dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator. With our choice of scaling the dynamics converges to a coupled SDE-ODE s…
A new high-frequency market making strategy using Deep Hawkes process.
problem Optimizing high-frequency trading in volatile markets.
method Developed a Deep Hawkes process to model order arrivals and their effects on the limit order book.
result The new strategy outperforms traditional methods in market making.
The paper proposes a new model for financial order books without assuming prices or quantities.
problem Understanding the geometry of financial order books without assuming prices or quantities.
method Modeling financial order books as an inflationary relational system without metric, temporal, or price coordinates. Observable quantities arise through spectral embeddings of the graph Laplacian.
result Projected supply and demand are constrained to gamma-like functional forms, which can be observed as integrated-gamma cumulative profiles in high-frequency data.
Study on LOB dynamics using mean-field game theory.
problem Modeling liquidity dynamics in limit order books.
method Mean-field stochastic differential equation and control problem formulation.
result Equilibrium density function of LOB can be derived.
We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity ) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume and . The dependence …
A framework models order book dynamics using point processes and mass transport.
problem Capturing the complex dynamics of limit order books.
method Combines spatial point process for order flow and mass transport operator for market clearing.
result Provides insights into the interplay between order flow and price dynamics.
We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a n…
We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity solutions linked to order book formation and recovery is explored. The main result…
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in ph…
Derives operational-time variance kernel for reaction boundaries in financial markets.
problem Separating components in volatility models to better understand market dynamics.
method Derives a variance kernel for a latent-order-book reaction boundary, separating structural boundary cumulant, clock projection, and pricing-measure choice.
result Operational variance has a closed asymptotic form for long-memory forcing, with effective signed-forcing intensity and resilience.
Two price regimes identified in limit order books: close and far from quotes.
problem Understanding the distribution and behavior of limit orders in limit order books.
method Analysis of limit order book data in dimensions of price, time, lifetime, and volume.
result Identification of two distinct regimes in the limit order book: close and far from quotes.
Modeling high-frequency order book data with Hawkes-Markovian process.
problem Capturing the dynamics of high-frequency order book events.
method Hawkes process with Markovian baseline intensities, LASSO regularization, and Akaike Information Criteria.
result Effective modeling of order book dynamics with reduced parameter redundancy.
The paper analyzes fill probabilities in limit order books with varying price levels.
problem Determining the likelihood of limit orders being executed in a limit order book.
method Developed a state-dependent stochastic framework to model limit order book dynamics.
result Derived semi-analytical expressions for fill probabilities and mid-price changes.
An Empirical Analysis on Financial Markets: Insights from the Application of Statistical Physicsq-fin.TR
Model uses statistical physics principles to predict financial market volatility and returns.
problem Predicting price volatility and expected returns in financial markets.
method Inspired by statistical physics, the study introduces a physical model using Level 3 order book data to measure kinetic energy and momentum.
result The model outperforms traditional and machine learning approaches in forecasting volatility and expected returns.
Latent order book models have allowed for significant progress in our understanding of price formation in financial markets. In particular they are able to reproduce a number of stylized facts, such as the square-root impact law. An important question that is raised -- if one is to bring such models closer to real mark…
We present a general Markovian framework for order book modeling. Through our approach, we aim at providing a tool enabling to get a better understanding of the price formation process and of the link between microscopic and macroscopic features of financial assets. To do so, we propose a new method of order book repre…
The order book as a queueing system: average depth and influence of the size of limit ordersq-fin.TR
We study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponential. Although simplistic, the model provides an analytical tractability that should not be overlooked. Using basic result…
Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…
Deep learning predicts stock price changes in Limit Order Books.
problem Predicting high-frequency Limit Order Book mid-price changes.
method Cutting-edge deep learning methodologies applied to NASDAQ stocks.
result Deep learning methods' effectiveness varies by stock microstructure.
Model simulates correlation emergence in two coupled limit order books.
problem Modeling correlation emergence in coupled limit order books.
method Simulated two coupled diffusive limit order books using random walks in the fluid limit, with trader interactions.
result Demonstrated the recovery of an Epps effect from the model.
Exchange uses incentives to optimize limit order book dynamics.
problem Optimizing market liquidity in fragmented electronic markets.
method Modeling limit order book as SPDE and using control theory to design incentives.
result Exchange can design incentives to modify order book shape and increase liquidity.
We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation (SPDE) with multiplicative noise for the order book centered at the mid-price, along with stochastic dynamics for the mid-price which is consistent with the order flo…
Transformers predict price movements from limit order books.
problem Predicting price movements from limit order books.
method Causal convolutional network with masked self-attention.
result Significantly outperforms existing architectures on FI-2010 dataset.
Revises mean-field theory of Santa Fe model using kinetic theory.
problem Deriving a solid mathematical foundation for the Santa Fe model.
method Systematic derivation of BBGKY hierarchy from exact master equation.
result Explicit and closed-form solutions for mean-field equations.
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 Exchange. As a result, the limit price is broadly distributed around the best price acc…
The existing literature provides evidence that limit order book data can be used to predict short-term price movements in stock markets. This paper proposes a new neural network architecture for predicting return jump arrivals in equity markets with high-frequency limit order book data. This new architecture, based on …
The paper examines the reliability of limit order book representations in the face of data perturbation.
problem The reliability of limit order book representations under data perturbation.
method Experimental analysis of existing representations and guidelines for future research.
result Existing representations of limit order book data are vulnerable to data perturbation.
The distribution of returns in financial time series exhibits heavy tails. In empirical studies, it has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an agent based model to study this issue and, in particular, how the gaps in the order …
When modelling stock market dynamics, the price formation is often based on an equilbrium mechanism. In real stock exchanges, however, the price formation is goverend by the order book. It is thus interesting to check if the resulting stylized facts of a model with equilibrium pricing change, remain the same or, more g…
Study shows gaps in Bitcoin order book are linked to returns but only in the short term.
problem Understanding the relationship between gaps and returns in Bitcoin order books.
method Examined the dynamics of gaps and returns in a Bitcoin order book without considering long-term causation.
result The causal relationship between gaps and returns is limited to instantaneous causation.
This paper consists of two parts. The first part is devoted to empirical analysis of consolidated order book (COB) for the index RTS futures. In the second part we consider Poissonian multi--agent model of the COB. By varying parameters of different groups of agents submitting orders to the book we are able to model va…
Simulates financial market orders using anomalous diffusion models.
problem Anomalous diffusion in financial market order dynamics.
method Discrete Time Random Walk with Sibuya waiting times, non-uniform sampling, and cubic spline interpolation.
result Demonstrates price impact for different forcing functions and model parameters.
This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient and specifically designed to take advantage of the spatial structure of limit order books. The new architecture yields a low-dimensional model of price movements deep …
Unified analytic account of correlation emergence and Epps effect in coupled limit order books
problem Correlation emergence and Epps effect in coupled limit order books
method Discrete random-walk description of order flow with creation, cancellation, and diffusion, coupled reaction-diffusion equations with moving reaction boundary
result Realized correlations as a function of aggregation time
Deep learning predicts Bitcoin spot price movements from order books.
problem Predicting cryptocurrency spot price movements from order book data.
method Temporal CNNs trained on 2-second prediction time horizon.
result 71% walk-forward accuracy on coinbase data.
Simulates realistic execution and costs in limit order books.
problem Realistic simulation of limit order books for large-tick assets.
method Tractable representation of spread and volume imbalance; calibrated event timing; feedback mechanism for market impact.
result Simulator yields realistic behavior and sensitivity to execution parameters.
We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism used in stock markets. Both buyers and sellers are elastic in the price-quantity …
We build an agent-based model for the order book with three types of market participants: informed trader, noise trader and competitive market makers. Using a Glosten-Milgrom like approach, we are able to deduce the whole limit order book (bid-ask spread and volume available at each price) from the interactions between…
We develop a second-order model for limit order books in a single scaling regime.
problem Modeling price and volume dynamics in a limit order book with market and limit orders at a common time scale.
method Established a first- and second-order approximation for an infinite dimensional limit order book model.
result Proved the existence and uniqueness of a solution for the second-order approximation.
Limit Order Book (LOB) shape modeling in presence of heterogeneously informed market participantsq-fin.TR
Paper models limit order book with informed traders and market makers.
problem Modeling the limit order book with heterogeneous market participants.
method Agent-based model with four types of participants: informed traders, noise traders, informed market makers, and noise market makers. Based on Glosten-Milgrom and Huang-Rosenbaum-Saliba approaches.
result Derived the static limit order book characteristics and compared them with existing models.
Study integrates deep learning with financial data for improved trading strategies.
problem Enhancing predictive performance in algorithmic trading and portfolio optimization.
method Developed embedding techniques to treat limit order book snapshots as image-based input channels.
result Achieved state-of-the-art performance in high-frequency trading algorithms.