限价订单市场的半马尔可夫模型
A Semi-Markovian Modeling of Limit Order Markets
摘要：
R. Cont和A. de Larrard（SIAM J. Finan. Math，2013）引入了一个用于限价订单簿动态的易处理的随机模型，计算各种感兴趣的量，例如价格上涨的概率或价格过程的扩散极限。正如经验观察所建议的那样，我们将他们的框架扩展到1）书籍事件到达间隔时间的任意分布（可能是非指数分布）和2）新书事件及其相应到达间隔时间的性质都取决于前一本书事件的性质。我们这样做，通过诉诸马尔可夫更新过程建模的动态出价和要求队列。我们通过各种感兴趣量的拉普拉斯变换的显式表达式来保持分析的易处理性。我们通过将我们的模型校准到2012年6月21日的五只股票亚马逊，苹果，谷歌，英特尔和微软来证明和说明我们的方法。在R。Cont和A. de Larrard的方法中，买卖价差保持恒定等于一个刻度，仅对买卖队列进行建模（它们彼此独立，并在价格变化后重新初始化），并且所有订单具有相同的大小。
英文摘要：
R. Cont and A. de Larrard (SIAM J. Finan. Math, 2013) 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 inter-arrival times (possibly non-exponential) and 2) both the nature of a new book event and its corresponding inter-arrival 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 and Microsoft on June 21^{st} 2012. As in R. Cont and A. de Larrard, the bid-ask spread remains constant equal to one tick, only the bid and ask queues are modeled (they are independent from each other and get reinitialized after a price change), and all orders have the same size.
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