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Black-Scholes equation from Gauge Theory of Arbitrage

Author

Listed:
  • Kirill Ilinski

    (University of Birmingham)

  • Gleb Kalinin

    (IPhys Group, St-Petersburg)

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.

Suggested Citation

  • Kirill Ilinski & Gleb Kalinin, 1997. "Black-Scholes equation from Gauge Theory of Arbitrage," Papers hep-th/9712034, arXiv.org, revised Oct 1998.
    • Handle: RePEc:arx:papers:hep-th/9712034
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    Cited by:

    1. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.

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