Related papers: Correlation emergence in two coupled simulated lim…
In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling…
We analyse the dependence of stock return cross-correlations on the sampling frequency of the data known as the Epps effect: For high resolution data the cross-correlations are significantly smaller than their asymptotic value as observed…
Time and the choice of measurement time scales is fundamental to how we choose to represent information and data in finance. This choice implies both the units and the aggregation scales for the resulting statistical measurables used to…
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 extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic…
We propose a new model for the level I of a Limit Order Book (LOB), which incorporates the information about the standing orders at the opposite side of the book after each price change and the arrivals of new orders within the spread. Our…
The Epps effect, the decrease of correlations between stock returns for short time windows, was traced back to the trading asynchronicity and to the occasional lead-lag relation between the prices. We study pairs of stocks where the latter…
Motivated by a zero-intelligence approach, the aim of this paper is to connect the microscopic (discrete price and volume), mesoscopic (discrete price and continuous volume) and macroscopic (continuous price and volume) frameworks for the…
A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. We focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a…
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…
It is a well-documented fact that the correlation function of the returns on two "related" assets is generally increasing as a function of the horizon $h$ of these returns. This phenomenon, termed the Epps Effect, holds true in a wide…
In this article, we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). We use the proposed modeling…
In this work, we present a continuous-time large-population game for modeling market microstructure betweentwo consecutive trades. The proposed modeling framework is inspired by our previous work [23]. In this framework, the Limit Order…
We study the dynamics of the limit order book of liquid stocks after experiencing large intra-day price changes. In the data we find large variations in several microscopical measures, e.g., the volatility the bid-ask spread, the bid-ask…
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…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
We review the decomposition method of stock return cross-correlations, presented previously for studying the dependence of the correlation coefficient on the resolution of data (Epps effect). Through a toy model of random walk/Brownian…
We present a method to compensate statistical errors in the calculation of correlations on asynchronous time series. The method is based on the assumption of an underlying time series. We set up a model and apply it to financial data to…
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…
In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or…