Related papers: A Mathematical Approach to Order Book Modeling
We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a…
The order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order-driven markets. We investigate the dynamics of order cancelation by studying the statistical properties of…
In this study, we introduce a physical model inspired by statistical physics for predicting price volatility and expected returns by leveraging Level 3 order book data. By drawing parallels between orders in the limit order book and…
In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator…
Buying and selling stocks causes price changes, which are described by the price impact function. To explain the shape of this function, we study the Island ECN orderbook. In addition to transaction data, the orderbook contains information…
A micro-scale model is proposed for the evolution of the limit order book. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of bid…
The tatonnement process in high frequency order driven markets is modeled as a search by buyers for sellers and vice-versa. We propose a total order book model, comprising limit orders and latent orders, in the absence of a market maker. A…
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…
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…
We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow…
We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The…
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…
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…
We compare the predictions of the stationary Kyle model, a microfounded multi-step linear price impact model in which market prices forecast fundamentals through information encoded in the order flow, with those of the propagator model, a…
In this paper, we study the offline sequential feature-based pricing and inventory control problem where the current demand depends on the past demand levels and any demand exceeding the available inventory is lost. Our goal is to leverage…
The paper tests the validity of the critique of the fiscal theory of the price level. A stochastic general equilibrium model with continuous time is constructed. An active fiscal policy and a passive monetary policy have been set. Monetary…
We generalise the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting and annihilating particles by presenting a model of the velocity on each side (buy…
We consider a simple model for the evolution of a limit order book in which limit orders of unit size arrive according to independent Poisson processes. The frequencies of buy limit orders below a given price level, respectively sell limit…
We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we…
Order submission and cancellation are two constituent actions of stock trading behaviors in order-driven markets. Order submission dynamics has been extensively studied for different markets, while order cancellation dynamics is less…