B1402
Title: Markov chain modeling of a limit order book with limit order arrivals following Markov modulated Poisson processes
Authors: Daniel Miao - National Taiwan University of Science and Technology (Taiwan) [presenting]
Abstract: A limit order book queueing system is considered where the arrival processes of the limit bid and ask orders are modelled by Markov-modulated Poisson processes (MMPP). In contrast with the traditional model where the order arrivals are modelled by Poisson processes, the Markov switching nature of the extended model helps to reflect the clustering behaviours of order arrival processes. The queueing dynamics of such a system are modelled by a multidimensional, birth-death type Markov chain, for which the probability distributions of the state variables can be obtained from its generator matrix by standard matrix computation procedure. By properly assigning absorbing states in the Markov chain, the distributions of the first passage times are computed so that the bid and ask queues become empty. The techniques are then applied to compute two key probabilities in high-frequency trading: the probability of the price going up and the probability of order execution before the price moves. In the numerical analysis, it is investigated how the two key probabilities are influenced by the clustered nature of the limit order arrival processes. Results show that significant impacts are observed on the two probabilities when the arrival processes deviate from the Poisson process to MMPP.
