Related papers: Ergodicity and diffusivity of Markovian order book…
This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion…
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 present a Markovian market model driven by a hidden Brownian efficient price. In particular, we extend the queue-reactive model, making its dynamics dependent on the efficient price. Our study focuses on two sub-models: a signal-driven…
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…
Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time…
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…
We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity…
We study a phenomenological model for the continuous double auction, equivalent to two independent $M/M/1$ queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the…
This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classify intraday order book trading events into a range of categories based on their order types and the price…
An agent-based model for financial markets has to incorporate two aspects: decision making and price formation. We introduce a simple decision model and consider its implications in two different pricing schemes. First, we study its…
We propose a modeling framework for the dynamics of a reduced form order book in event time and based on event sizes. Our framework for the order book is influenced by [9], but compared to [9] we allow the best bid ask spread to be larger…
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…
We introduce a simple framework in which market participants update their prior about an efficient price with a model-based learning process. We show that exponential intensities for the arrival of aggressive orders arise naturally in this…
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 limit order book, where buyers and sellers register to trade a security at specific prices. The largest price buyers on the book are willing to offer is called the market bid price, and the smallest price sellers on the book…
In this work, we consider a continuous-time inventory system where the demand process follows an inventory-dependent diffusion process. The ordering cost of each order depends on the order quantity and is given by a general function, which…
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…
Equity auctions display several distinctive characteristics in contrast to continuous trading. As the auction time approaches, the rate of events accelerates causing a substantial liquidity buildup around the indicative price. This, in…
This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the…
Understanding the micro-dynamics of asset prices in modern electronic order books is crucial for investors and regulators. In this paper, we use an order by order Eurostoxx database spanning over 3 years to analyze the joint dynamics of…