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Black-Scholes equation from Gauge Theory of Arbitrage

Kirill Ilinski·Gleb Kalinin
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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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Kirill Ilinski, Gleb Kalinin. 1998-10-26. Black-Scholes equation from Gauge Theory of Arbitrage. https://arxiv.org/abs/hep-th/9712034

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