Symmetries of the Black-Scholes equation

TL;DR

This paper explores the symmetries of the Black-Scholes equation by identifying its algebra of isovectors, leading to new transformation families that can be applied to solutions.

Contribution

It determines the algebra of isovectors for the Black-Scholes equation, revealing new solution transformations not previously known.

Findings

Identified the algebra of isovectors for the Black-Scholes equation

Discovered new families of transformations on solutions

Enhanced understanding of the equation's symmetry structure

Abstract

We determine the algebra of isovectors for the Black--Scholes equation. As a consequence, we obtain some previously unknown families of transformations on the solutions.