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A model for the evolution of an order book

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We model an order book as a vector-valued continuous-time Markov chain tracking the number of limit orders in the book at each price. We describe an estimation procedure for our model parameters, based on the level II trade and quotes data, and apply it to various stocks traded on the Tokyo stock exchange. We then validate our model by comparing (i) one-step transition probabilities (ii) the daily return distributions and (iii) the long term order book shape for the original data and the simulated data. Moreover, we present techniques from the queuing theory literature that provide methods to compute probabilities of various microstructure events of interest to technical trading in an order book.

This talk is part of the Probability series.

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