Market Mill Dependence Pattern in the Stock Market: Modeling of Predictability and Asymmetry via Multi-Component Conditional Distribution
Abstract
Recent studies have revealed a number of striking dependence patterns in high frequency stock price dynamics characterizing probabilistic interrelation between two consequent price increments x (push) and y (response) as described by the bivariate probability distribution P(x,y) [1,2,3,4]. There are two properties, the market mill asymmetries of P(x,y) and predictability due to nonzero z-shaped mean conditional response, that are of special importance. Main goal of the present paper is to put together a model reproducing both the z-shaped mean conditional response and the market mill asymmetry of P(x,y) with respect to the axis y=0. We develop a probabilistic model based on a multi-component ansatz for conditional distribution P(y|x) with push-dependent weights and means describing both properties. A relationship between the market mill asymmetry and predictability is discussed. A possible connection of the model to agent-based picture is outlined.
Keywords
Cite
@article{arxiv.physics/0701158,
title = {Market Mill Dependence Pattern in the Stock Market: Modeling of Predictability and Asymmetry via Multi-Component Conditional Distribution},
author = {Andrei Leonidov and Vladimir Trainin and Alexander Zatsev and Sergey Zaitsev},
journal= {arXiv preprint arXiv:physics/0701158},
year = {2009}
}