Appearances of pseudo-bosons from Black-Scholes equation

TL;DR

This paper explores how pseudo-bosons emerge from the Black-Scholes equation's Schrödinger form and their role in computing the pricing kernel, offering a novel mathematical perspective on option pricing.

Contribution

It introduces the application of pseudo-bosons to the Black-Scholes equation, providing a new framework for analyzing the pricing kernel in financial mathematics.

Findings

Pseudo-bosons naturally arise in the Schrödinger representation of the Black-Scholes equation.

Pseudo-bosons can be used to compute the pricing kernel.

The approach offers a new mathematical perspective on option pricing.

Abstract

It is a well known fact that the Black-Scholes equation admits an alternative representation as a Schr\"odinger equation expressed in terms of a non self-adjoint hamiltonian. We show how {\em pseudo-bosons}, linear or not, naturally arise in this context, and how they can be used in the computation of the pricing kernel.