(Submitted on 1 Jul 2018)
Since Bachelier's thesis in 1900, when mathematical finance began, attempts at understanding the nature of stock market prices and at predicting them have not succeeded. Statistical models have only found minor regularities and anomalies. Other approaches have failed or are illusory. To this day, physicists and mathematicians working in economy consider that the evolution of security prices is largely random, and, thus, not predictable. We show that not only is the evolution of security prices not random but it is semi-deterministic and, more remarkably, governed by a physical law.
The law takes the form of a physicomathematical theory centered around a purely mathematical function (not a model and unrelated to statistical methods). The function, which can be described as an "isodense" network of "moving" regression curves of an order greater than or equal to 1, can be conveniently represented graphically. The graphical representation, called a "topological network", reveals the existence of new mathematical objects, which emerge spontaneously (they are not mathematically drawn).
What is remarkable is that these objects, called "characteristic figures", mainly "cords", have the unique property of attracting and repelling the price, so that the price bounces from one cord to another. The direct consequence is that prices are driven by these cords in a semi-deterministic manner (leaning towards deterministic). We can say that we now understand the reason behind price movements and can predict stock prices both qualitatively and quantitatively. Note that time series data (not limited to financial) is input directly into the function without any fitting. The function is universal (it is a one fits all function) and, thanks to its extreme sensitivity, reveals the hidden order present in time series data that other methods have never uncovered.arXiv download page