Market Dynamics. On a Muse of Cash Flow and Liquidity Deficit

Abstract

A first attempt at obtaining market--directional information from a non--stationary solution of the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" [1] is presented. We demonstrate that the concept of price impact is poorly applicable to market dynamics. Instead, we consider the execution flow $I=dV/dt$ operator with the "impact from the future" term providing information about not--yet--executed trades. The "impact from the future" on $I$ can be directly estimated from the already--executed trades, the directional information on price is then obtained from the experimentally observed fact that the $I$ and $p$ operators have the same eigenfunctions (the exact result in the dynamic impact approximation $p=p(I)$). The condition for "no information about the future" is found and directional prediction quality is discussed. This work makes a substantial contribution toward solving the ultimate market dynamics problem: find evidence of existence (or proof of non--existence) of an automated trading machine which consistently makes positive P\&L on a free market as an autonomous agent (aka the existence of the market dynamics equation). The software with a reference implementation of the theory is provided.