Related papers: Fill Probabilities in a Limit Order Book with Stat…
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both…
Market participants regularly send bid and ask quotes to exchange-operated limit order books. This creates an optimization challenge where their potential profit is determined by their quoted price and how often their orders are…
The distribution of liquidity within the limit order book is essential for the impact of market orders on the stock price and the emergence of price shocks. Limit orders are characterized by stylized facts: The number of inserted limit…
We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical…
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…
We examine the dynamics of the bid and ask queues of a limit order book and their relationship with the intensity of trade arrivals. In particular, we study the probability of price movements and trade arrivals as a function of the quote…
In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this article we consider a limit order book model that allows for time-dependent, deterministic depth and resilience of the book and…
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 study a microscopic limit order book model, in which the order dynamics depend on the current best bid and ask price and the current volume density functions, simultaneously, and derive its macroscopic high-frequency dynamics. As opposed…
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…
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…
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 placement tactics play a crucial role in high-frequency trading algorithms and their design is based on understanding the dynamics of the order book. Using high quality high-frequency data and a set of microstructural features, we…
I present an overview of some recent advancements on the empirical analysis and theoretical modeling of the process of price formation in financial markets as the result of the arrival of orders in a limit order book exchange. After…
We investigate the behavior of limit order books on the meso-scale motivated by order execution scheduling algorithms. To do so we carry out empirical analysis of the order flows from market and limit order submissions, aggregated from…
We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show…
Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This…
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…
Through the analysis of a dataset of ultra high frequency order book updates, we introduce a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data. To do…
We present a general framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a…