1997•RePEc: Research Papers in EconomicsOpen access

Black-Scholes equation from Gauge Theory of Arbitrage

Kirill Ilinski, Gleb Kalinin

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.

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Key concepts: Arbitrage, Black–Scholes model, Mathematics, Arbitrage pricing theory, Constraint (computer-aided design), Mathematical economics, Derivative (finance), Stochastic differential equation