GENERAL SEMI-MARKOV MODEL FOR LIMIT ORDER BOOKS

The paper considers a general semi-Markov model for limit order books with two states that incorporates price changes that are not fixed to one tick. Furthermore, we introduce an even more general case of the semi-Markov model for limit order books that incorporates an arbitrary number of states for the price changes. For both cases, the justifications, diffusion limits, implementations and numerical results are presented for different limit order book data: Apple, Amazon, Google, Microsoft, Intel on 21 June 2012 and Cisco, Facebook, Intel, Liberty Global, Liberty Interactive, Microsoft, Vodafone from 3 November 2014 to 7 November 2014.