The amazing power of dimensional analysis: Quantifying market impact
Abstract
This note complements the inspiring work on dimensional analysis and market microstructure by Kyle and Obizhaeva [18]. Following closely these authors, our main result shows by a similar argument as usually applied in physics the following remarkable fact. If the market impact of a meta-order only depends on four well-defined and financially meaningful variables, then -- up to a constant -- there is only one possible form of this dependence. In particular, the market impact is proportional to the square-root of the size of the meta-order. This theorem can be regarded as a special case of a more general result of Kyle and Obizhaeva. These authors consider five variables which might have an influence on the size of the market impact. In this case one finds a richer variety of possible functional relations which we precisely characterize. We also discuss the analogies to classical arguments from physics, such as the period of a pendulum.
Keywords
Cite
@article{arxiv.1702.05434,
title = {The amazing power of dimensional analysis: Quantifying market impact},
author = {Mathias Pohl and Alexander Ristig and Walter Schachermayer and Ludovic Tangpi},
journal= {arXiv preprint arXiv:1702.05434},
year = {2017}
}
Comments
Revised version