Physics – Physics and Society
Scientific paper
2007-01-14
Physics
Physics and Society
Scientific paper
10.1016/j.physa.2007.07.062
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.
Leonidov Andrei
Trainin Vladimir
Zaitsev Sergey
Zatsev Alexander
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