On the formalization of order flow toxicity on financial markets

The paper considers the microstructural order flow model for financial markets. The order flow imbalance process is used as an integral indicator of the current state of the limit-order book. The model of order flow imbalance is used to analyze the properties of the current limit-order book state, which is considered as two-sided risk process with stochastic premiums. The concept of order flow toxicity on financial markets is studied. This concept is formalized with probabilities of crossing fixed levels by the order flow imbalance process. The paper introduces the concepts of the instantaneous toxicity profile and Bayesian and quantile indicators of toxicity. These indicators are calculated for two model types of order flows: the first one has unit volume orders and the second one consists of orders with random volume which has exponential distribution.