Black-Scholes equation from Gauge Theory of Arbitrage
High Energy Physics - Theory
2009-02-20 v2 Statistical Mechanics
High Energy Physics - Lattice
Physics and Society
Pricing of Securities
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.
Keywords
Cite
@article{arxiv.hep-th/9712034,
title = {Black-Scholes equation from Gauge Theory of Arbitrage},
author = {Kirill Ilinski and Gleb Kalinin},
journal= {arXiv preprint arXiv:hep-th/9712034},
year = {2009}
}
Comments
Latex, 19 pages