Abstract
R. Cont and A. de Larrard [SIAM J. Financial Math., 4 (2013), pp. 1--25] introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion limit of the price process. As suggested by empirical observations, we extend their framework to (1) arbitrary distributions for book events interarrival times (possibly nonexponential) and (2) both the nature of a new book event and its corresponding interarrival time depend on the nature of the previous book event. We do so by resorting to Markov renewal processes to model the dynamics of the bid and ask queues. We keep analytical tractability via explicit expressions for the Laplace transforms of various quantities of interest. We justify and illustrate our approach by calibrating our model to the five stocks Amazon, Apple, Google, Intel, Microsoft on June 21, 2012, to the 15 stocks from Deutsche Borse Group (September 23, 2013) and to CISCO asset (Nov...
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