Relativistic Black-Scholes model

TL;DR

This paper introduces a relativistic extension of the Black-Scholes model derived from relativistic quantum mechanics, leading to a volatility smile effect, and applies it to European vanilla options.

Contribution

It presents a novel relativistic Black-Scholes model based on the telegraphers equation, connecting financial modeling with relativistic quantum mechanics.

Findings

Volatility smile effect observed in the model

Relativistic extension captures local effects in option pricing

Model provides a new perspective on option volatility dynamics

Abstract

Black-Scholes equation, after a certain coordinate transformation, is equivalent to the heat equation. On the other hand the relativistic extension of the latter, the telegraphers equation, can be derived from the Euclidean version of the Dirac equation. Therefore the relativistic extension of the Black-Scholes model follows from relativistic quantum mechanics quite naturally. We investigate this particular model for the case of European vanilla options. Due to the notion of locality incorporated in this way one finds that the volatility frown-like effect appears when comparing to the original Black-Scholes model.