Related papers: Modeling high-frequency order flow imbalance by fu…
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…
Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations…
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…
The optimal power flow (OPF) problem is an important mathematical program that aims at obtaining the best operating point of an electric power grid. The optimization problem typically minimizes the total generation cost subject to certain…
This paper presents a method for forecasting limit order book durations using a self-exciting flexible residual point process. High-frequency events in modern exchanges exhibit heavy-tailed interarrival times, posing a significant challenge…
We introduce and treat rigorously a new multi-agent model of the continuous double auction or in other words the order book (OB). It is designed to explain collective behaviour of the market when new information affecting the market…
Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduce a framework to analyze the market price of liquidity risk, which allows us to derive an inhomogeneous Bernoulli ordinary differential…
At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price,...). Thus, in practice, market participants face the problem…
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…
We establish a first and second-order approximation for an infinite dimensional limit order book model (LOB) in a single (''critical'') scaling regime where market and limit orders arrive at a common time scale. With our choice of scaling…
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…
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…
Standard models in economics stress the role of intelligent agents who maximize utility. However, there may be situations where, for some purposes, constraints imposed by market institutions dominate intelligent agent behavior. We use data…
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…
In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a…
The estimation of the volatility with high-frequency data is plagued by the presence of microstructure noise, which leads to biased measures. Alternative estimators have been developed and tested either on specific structures of the noise…
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…
A recent analysis of empirical limit order flow data highlights the necessity for a more refined order flow model that integrates the power-law distribution of limit order cancellation times. These cancellation times follow a discrete…
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls…
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…