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Derivative pricing with virtual arbitrage

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  • Kirill Ilinski
  • Alexander Stepanenko

Abstract

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equation which, in the absence of the virtual arbitrage or for an infinitely fast market reaction, reduces to the Black-Scholes equation. Explicit formulas are obtained for European call and put vanilla options.

Suggested Citation

  • Kirill Ilinski & Alexander Stepanenko, 1999. "Derivative pricing with virtual arbitrage," Papers cond-mat/9902046, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/9902046
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    Cited by:

    1. Kirill Ilinski, 1999. "How to account for virtual arbitrage in the standard derivative pricing," Papers cond-mat/9902047, arXiv.org.
    2. Kirill Ilinski, 1999. "Virtual Arbitrage Pricing Theory," Finance 9902001, University Library of Munich, Germany.
    3. Contreras G., Mauricio, 2021. "Endogenous stochastic arbitrage bubbles and the Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    4. Mauricio Contreras & Rely Pellicer & Daniel Santiagos & Marcelo Villena, 2015. "Calibration and simulation of arbitrage effects in a non-equilibrium quantum Black-Scholes model by using semiclassical methods," Papers 1512.05377, arXiv.org.
    5. Mauricio Contreras G. & Roberto Ortiz H, 2021. "Three little arbitrage theorems," Papers 2104.10187, arXiv.org.
    6. Jimmy E. Hilliard & Jitka Hilliard, 2017. "Option pricing under short-lived arbitrage: theory and tests," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1661-1681, November.
    7. Mauricio Contreras G, 2020. "Endogenous Stochastic Arbitrage Bubbles and the Black--Scholes model," Papers 2009.09329, arXiv.org.

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