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Random walk model from the point of view of algorithmic trading

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  • Oleh Danyliv
  • Bruce Bland
  • Alexandre Argenson

Abstract

Despite the fact that an intraday market price distribution is not normal, the random walk model of price behaviour is as important for the understanding of basic principles of the market as the pendulum model is a starting point of many fundamental theories in physics. This model is a good zero order approximation for liquid fast moving markets where the queue position is less important than the price action. In this paper we present an exact solution for the cost of the static passive slice execution. It is shown, that if a price has a random walk behaviour, there is no optimal limit level for an order execution: all levels have the same execution cost as an immediate aggressive execution at the beginning of the slice. Additionally the estimations for the risk of a limit order as well as the probability of a limit order execution as functions of the slice time and standard deviation of the price are derived.

Suggested Citation

  • Oleh Danyliv & Bruce Bland & Alexandre Argenson, 2019. "Random walk model from the point of view of algorithmic trading," Papers 1908.04333, arXiv.org.
    • Handle: RePEc:arx:papers:1908.04333
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    File URL: http://arxiv.org/pdf/1908.04333
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    Cited by:

    1. Ivan Letteri & Giuseppe Della Penna & Giovanni De Gasperis & Abeer Dyoub, 2022. "DNN-ForwardTesting: A New Trading Strategy Validation using Statistical Timeseries Analysis and Deep Neural Networks," Papers 2210.11532, arXiv.org.
    2. Ivan Letteri & Giuseppe Della Penna & Giovanni De Gasperis & Abeer Dyoub, 2022. "A Stock Trading System for a Medium Volatile Asset using Multi Layer Perceptron," Papers 2201.12286, arXiv.org.

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