A Correction Note for Price Dynamics in a Markovian Limit Order Market

Abstract

A previously published and widely quoted paper, Price Dynamics in a Markovian Limit Order Market, [SIAM J. Financial Math., 4 (2013), pp. 1--25] has provided analytic solutions for many interesting quantities for the price dynamics of the limit order book. However, for unbalanced order flow cases, one of its major results, the price increase probability conditional on the state of the limit order book, is found to be incorrect due to its citing an erroneous formula from another paper. We correct this error by proposing another analytical solution using the characteristic functions of probability distributions. The final analytical solution presented in this paper is of a simple form and easy to calculate.