From Market Jaws to the Newton Method: The Geometry of How a Market Can Solve Systems of Equations

Abstract

Since market equilibrium can be interpreted as a solution to a system of equations, "price discovery," as it called in the language of market makers, can be viewed as having "found" the solution. Of course the information needed to even formulate the equations does not exist in one place so the idea that markets are "searching" for the solution to a system of equations as a numerical process would search, cannot be taken literally. Nevertheless, it is interesting that the language that has evolved from the world of practical markets has such an interpretation and curiosity alone makes one wonder how markets settle on the particular pattern of prices that solve a particular system of equations.