The What, When and Where of Limit Order Books
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We model the limit order book (LOB) as a continuous Markov process and develop an algebra to describe its dynamics based on the fundamental events of the book: order arrivals and cancellations. We show how all observables (prices, returns, and liquidity measures) are governed by the same variables which also drive arrival and cancellation rates. The sensitivity of our model is evaluated in a simulation study and an empirical analysis. We estimate several linearized model specifications based on the theoretical description of the LOB and conduct in- and out-of-sample forecasts on several frequencies. The in-sample results based on contemporaneous information suggest that our model describes up to 90 R^2 still ranges at around 80 information enters the model, we still observe an adjusted R^2 in the range of 15 an accuracy of over 75 Out-of-sample, on average, we obtain R^2 values for the Mincer-Zarnowitz regression of around 2-3 documented in the literature.
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