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Arbitrage opportunities and their implications to derivative hedging

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  • Panayides, Stephanos

Abstract

We explore the role that random arbitrage opportunities play in hedging financial derivatives. We extend the asymptotic pricing theory presented by Fedotov and Panayides [Stochastic arbitrage return and its implication for option pricing, Physica A 345 (2005) 207–217] for the case of hedging a derivative when arbitrage opportunities are present in the market. We restrict ourselves to finding hedging confidence intervals that can be adapted to the amount of arbitrage risk an investor will permit to be exposed to. The resulting hedging bands are independent of the detailed statistical characteristics of the arbitrage opportunities.

Suggested Citation

  • Panayides, Stephanos, 2006. "Arbitrage opportunities and their implications to derivative hedging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 289-296.
    • Handle: RePEc:eee:phsmap:v:361:y:2006:i:1:p:289-296
    DOI: 10.1016/j.physa.2005.06.077
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    References listed on IDEAS

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    1. Galai, Dan, 1977. "Tests of Market Efficiency of the Chicago Board Options Exchange," The Journal of Business, University of Chicago Press, vol. 50(2), pages 167-197, April.
    2. Matthias Otto, 2000. "Towards Non-Equilibrium Option Pricing Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 565-565.
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    4. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    5. Fedotov, Sergei & Panayides, Stephanos, 2005. "Stochastic arbitrage return and its implication for option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 207-217.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
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    Cited by:

    1. Contreras, Mauricio & Montalva, Rodrigo & Pellicer, Rely & Villena, Marcelo, 2010. "Dynamic option pricing with endogenous stochastic arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3552-3564.
    2. Contreras, M. & Echeverría, J. & Peña, J.P. & Villena, M., 2020. "Resonance phenomena in option pricing with arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Mauricio Contreras G, 2020. "Endogenous Stochastic Arbitrage Bubbles and the Black--Scholes model," Papers 2009.09329, arXiv.org.
    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. Contreras, Mauricio & Pellicer, Rely & Villena, Marcelo & Ruiz, Aaron, 2010. "A quantum model of option pricing: When Black–Scholes meets Schrödinger and its semi-classical limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5447-5459.
    6. Contreras G., Mauricio, 2021. "Endogenous stochastic arbitrage bubbles and the Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

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