Signs of market orders and human dynamics
Signs of market orders and human dynamics
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DOI：
10.1007/978-3-319-20591-5_4
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Joshin Murai
中科院分区：
文献类型：
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作者：
Joshin Murai
一个时间序列的市场订单的迹象被发现表现出长记忆。对于这一现象的起源有几种解释。一个令人信服的是，投资者倾向于在执行前将他们的大隐藏订单战略性地分割成小部分，以防止交易成本的增加。在这种解释下，已经提出了几个数学模型。在本文中，考虑到人类活动模式的突发性，我们提出了一个新的数学模型的顺序符号具有长记忆特性。此外，订单执行时间间隔分布的幂律指数被假定依赖于隐藏订单的大小。更准确地说，我们引入了一个离散时间随机过程，并证明了它的标度过程收敛于一个布朗运动和可数无穷多个Hurst指数大于1/2的分数布朗运动的叠加.
A time series of signs of market orders was found to exhibit long memory. There are several proposed explanations for the origin of this phenomenon. A cogent one is that investors tend to strategically split their large hidden orders into small pieces before execution to prevent the increase in the trading costs. Several mathematical models have been proposed under this explanation. In this paper, taking the bursty nature of the human activity patterns into account, we present a new mathematical model of order signs that have a long memory property. In addition, the power law exponent of distribution of a time interval between order executions is supposed to depend on the size of hidden order. More precisely, we introduce a discrete time stochastic process for polymer model, and show it’s scaled process converges to a superposition of a Brownian motion and countably infinite number of fractional Brownian motions with Hurst exponents greater than one-half.