Crossing Stocks and the Positive Grassmannian I: The Geometry behind Stock Market

Abstract

It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape. Still,the present paper will reveal the geometry behind the stock market transactions. The prices of market index (DJIA) stock components are arranged in ascending order from the smallest one in the left to the highest in the right. In such arrangement, as stock prices changes due to daily market quotations, it could be noticed that the price of a certain stock get over /under the price of a neighbor stock. These stocks are crossing. Arranged this way, the diagram of successive stock crossings is nothing else than a permutation diagram. From this point on the financial and combinatorial concepts are netted together to build a bridge connecting the stock market to a beautiful geometrical object that will be called stock market polytope. The stock market polytope is associated with the remarkable structure of positive Grassmannian . This procedure makes all the relevant information about the stock market encoded in the geometrical shape of the stock market polytope more readable.