Black-Scholes equation from Gauge Theory of Arbitrage

TL;DR

This paper applies Gauge Theory of Arbitrage to derivative pricing, deriving a modified Black-Scholes equation that accounts for virtual arbitrage and non-Brownian price dynamics, aligning more closely with real market data.

Contribution

It introduces a gauge-theoretic framework to extend the Black-Scholes model, incorporating arbitrage violations and complex price behaviors.

Findings

Standard Black-Scholes results are recovered from GTA.

Derived a nonlocal correction leading to an integro-differential equation.

Model captures non-Brownian and arbitrage effects observed in markets.

Abstract

We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators reaction on it. The model accounts for both violation of the no-arbitrage constraint and non-Brownian price walks which resemble real financial data. The correction is nonlocal and transform the differential Black-Scholes equation to an integro-differential one.