Signs of market orders and human dynamics

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Abstract

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.

Original languageEnglish
Title of host publicationSpringer Proceedings in Complexity
PublisherSpringer
Pages39-50
Number of pages12
DOIs
Publication statusPublished - Jan 1 2015

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ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation
  • Computer Science Applications

Cite this

Murai, J. (2015). Signs of market orders and human dynamics. In Springer Proceedings in Complexity (pp. 39-50). Springer. https://doi.org/10.1007/978-3-319-20591-5_4