Relativistic Quantum Finance

TL;DR

This paper introduces a relativistic quantum approach to finance by deriving a generalized Black-Scholes equation from the Klein-Gordon equation, revealing new invariance properties and a Cauchy distribution for stock prices.

Contribution

It proposes a novel relativistic quantum model for option pricing, extending classical models with conformal invariance and alternative stock price distributions.

Findings

Generalized Black-Scholes equation derived from Klein-Gordon equation

Invariance under conformal and scale transformations identified

Stock prices follow a Cauchy distribution in the invariant limit

Abstract

Employing the Klein-Gordon equation, we propose a generalized Black-Scholes equation. In addition, we found a limit where this generalized equation is invariant under conformal transformations, in particular invariant under scale transformations. In this limit, we show that the stock prices distribution is given by a Cauchy distribution, instead of a normal distribution.