Random Walk Model From the Point of View of Algorithmic Trading

12 Pages Posted: 13 Aug 2019

See all articles by Oleh Danyliv

Oleh Danyliv

Fidessa Group plc

Bruce Bland

Fidessa Group, London

Alexandre Argenson

Fidessa Group, London

Date Written: August 12, 2019

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.

Keywords: random walk, order book, best execution, limit order, execution cost

JEL Classification: G12, G14, G17

Suggested Citation

Danyliv, Oleh and Bland, Bruce and Argenson, Alexandre, Random Walk Model From the Point of View of Algorithmic Trading (August 12, 2019). Available at SSRN: https://ssrn.com/abstract=3436367 or http://dx.doi.org/10.2139/ssrn.3436367

Oleh Danyliv (Contact Author)

Fidessa Group plc ( email )

One Old Jewry
London, EC2R 8DN
United Kingdom

Bruce Bland

Fidessa Group, London ( email )

One Old Jewry
London, EC2R 8DN
United Kingdom

Alexandre Argenson

Fidessa Group, London ( email )

One Old Jewry
London, EC2R 8DN
United Kingdom

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