The Evolution of Security Prices Is Not Stochastic but Governed by a Physicomathematical Law

Since Bachelier's thesis in 1900 (laying the foundation of the stochastic process, or Brownian motion, as a model of stock price changes), attempts at understanding the nature of prices and at predicting them have failed. Statistical methods have only found minor regularities/anomalies, and other mathematical and physical approaches do not work. This leads researchers to consider that the evolution of security prices is basically random, and, thus, inherently not predictable. We show that the evolution of security prices is not a stochastic process but largely deterministic and governed by a physical law. The law takes the form of a physicomathematical theory centered around a purely mathematical function, unrelated to models and statistical methods. It can be described as an "isodense" network of moving regression curves of an order greater than or equal to 1. The salient aspect of the function is that, when inputting a time series of any security into the function, new mathematical objects emerge spontaneously, and these objects exhibit the unique property of attracting and repelling the quantity. The graphical representation of the function is called a "topological network" due to the preeminence of shapes over metrics, and the emergent objects are called "characteristic figures" (mainly "cords"). The attraction and repulsion of the price by the cords results in the price bouncing from cord to cord. Thus, the price has to be considered as driven by the cords in a semi-deterministic manner (leaning towards deterministic). With a function that describes the evolution of the price, we now understand the reason behind each price movement and can also predict prices both qualitatively and quantitatively. The function is universal, does not rely on any fitting, and, due to its extreme sensitivity, reveals the hidden order in financial time series data that existing research never uncovered.