Pseudo Hermitian formulation of Black-Scholes equation

TL;DR

This paper demonstrates that the Black-Scholes equation can be formulated as a pseudo-Hermitian system, allowing for a new mathematical perspective and explicit metric construction, linking it to pseudo supersymmetry.

Contribution

It introduces a pseudo-Hermitian formulation of the Black-Scholes equation and constructs the explicit metric operator, connecting it to pseudo supersymmetry.

Findings

Black-Scholes Hamiltonian is eta-pseudo Hermitian

Explicit metric operator eta is constructed

Black-Scholes Hamiltonian forms a pseudo supersymmetric system

Abstract

We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.