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Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading,…

This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and…

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…

Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free…

This paper explores the utility of agent-based simulations in realistically modelling market structures and sheds light on the nuances of optimal dealer strategies. It underscores the contrast between conclusions drawn from probabilistic…

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…

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982), corresponding to multiplicative maps, whose study has recently be revived recently in physics as a mechanism of…

In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…

An ability to postpone one's execution without penalty provides an important strategic advantage in high-frequency trading. To elucidate competition between traders one has to formulate to a quantitative theory of formation of the execution…

We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main…

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 an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 minutes) large price fluctuations are…

This letter treats of the power-law distribution of the sales of items. We propose a simple stochastic model which expresses a selling process of an item. This model produces a stationary power-law distribution, whose power-law exponent is…

In this paper, we present several heavy-tailed distributions belonging to the new class J of distributions obeying the principle of a single big jump introduced by Beck et al. [1]. We describe the structure of this class from different…

We develop a new market-making model, from the ground up, which is tailored towards high-frequency trading under a limit order book (LOB), based on the well-known classification of order types in market microstructure. Our flexible…

A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process…

Behavioral Finance has become a challenge to the scientific community. Based on the assumption that behavioral aspects of investors may explain some features of the Stock Market, we propose an agent based model to study quantitatively this…

This article introduces a general class of heavy-tailed autoregressions for modeling integer-valued time series with outliers. The proposed specification is based on a heavy-tailed mixture of negative binomial distributions that features an…

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the…

We present a detailed numerical analysis of the modified version of a conservative self-organized extremal model introduced by Pianegonda et. al. for the distribution of wealth of the people in a society. Here the trading process has been…