Schrödinger group and quantum finance

Abstract

Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black Scholes equation is invariant under Schrödinger group. In order to do this, the one dimensional free non-relativistic particle and its sym metries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schrödinger algebra representation is constructed.