Price Formation in Multilevel Semi-Markov Limit Order Markets

Nowadays a large volume of assets are traded in electronic, order driven markets, where all the information about buying and selling orders is condensed in a limit order book. Hence, there is an increasing need for parsimonious stochastic models that describe the dynamics of limit order books with applications ranging from devising high-frequency trading strategies to estimation and calibration of the model's parameters. We propose a tractable stochastic model for a multilevel limit order book in terms of a semi-Markov queuing system and develop the long-run dynamics of the resulting price process.