Statistical Modeling of High Frequency Financial Data: Facts, Models and Challenges

The availability of high-frequency data on transactions, quotes and order flow in electronic order-driven markets has revolutionized data processing and statistical modeling techniques in finance and brought up new theoretical and computational challenges. Market dynamics at the transaction level cannot be characterized solely in terms the dynamics of a single price and one must also take into account the interaction between buy and sell orders of different types by modeling the order flow at the bid price, ask price and possibly other levels of the limit order book.We outline the empirical characteristics of high-frequency financial time series and provide an overview of stochastic models for the continuous-time dynamics of a limit order book, focusing in particular on models which describe the limit order book as a queuing system. We describe some applications of such models and point to some open problems.

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