Recent works in the field of modeling information flows in contemporary high-frequency financial applications

Some results of recent studies in the field of modeling information flows in contemporary high-frequency financial systems and applications are discussed. In particular, the microscale model proposed by the authors is considered. Within the framework of this model, the order flows are described by doubly stochastic Poisson processes (also called Cox processes) which take account of the random character of intensities. To study the evolution of the limit order book (the current list of all active buy and sell orders), the models are proposed for the processes of number of orders imbalance and order flows imbalance having the form of two-sided risk processes, special compound Cox processes. These processes are sensitive indicators of the current state of the limit order book and provide the possibility to interpolate dynamics of the market between price changes, say, to trace toxicity of the order flow. The paper presents a review of main results obtained by application of these models.