Simulating and analyzing order book data: The queue-reactive 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 so, we split the time interval of interest into periods in which a well chosen reference price, typically the mid price, remains constant. Within these periods, we view the limit order book as a Markov queuing system. Indeed, we assume that the intensities of the order flows only depend on the current state of the order book. We establish the limiting behavior of this model and estimate its parameters from market data. Then, in order to design a relevant model for the whole period of interest, we use a stochastic mechanism that allows for switches from one period of constant reference price to another. Beyond enabling to reproduce accurately the behavior of market data, we show that our framework can be very useful for practitioners, notably as a market simulator or as a tool for the transaction cost analysis of complex trading algorithms

Critical behavior of a stochastic anisotropic Bak-Sneppen model

In this paper we present our study on the critical behavior of a stochastic anisotropic Bak-Sneppen (saBS) model, in which a parameter $\alpha$ is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness $f_c$ and the critical exponent $\tau_r$ by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents.Comment: 9 pages, 7 figures. arXiv admin note: text overlap with arXiv:cond-mat/9803068 by other author

Probability Metric Space on MV-Algebras

AbstractBy means of the probability measure theory of MV-algebras we introduce the concepts of probability truth degrees of the elements of MV-algebra and probability similarity degrees between elements, and then define therefrom three probability metric spaces on MV-algebra, and get some good results