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Option Pricing Beyond Black-Scholes Based on Double-Fractional Diffusion

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  • Hagen Kleinert
  • Jan Korbel

Abstract

We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the use of options whose prices were fixed by the Black-Scholes formula.

Suggested Citation

  • Hagen Kleinert & Jan Korbel, 2015. "Option Pricing Beyond Black-Scholes Based on Double-Fractional Diffusion," Papers 1503.05655, arXiv.org, revised Mar 2016.
    • Handle: RePEc:arx:papers:1503.05655
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    Cited by:

    1. Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
    2. Hinderks, W.J. & Wagner, A., 2019. "Pricing German Energiewende products: Intraday cap/floor futures," Energy Economics, Elsevier, vol. 81(C), pages 287-296.
    3. Victor Olkhov, 2020. "Classical Option Pricing and Some Steps Further," Papers 2004.13708, arXiv.org, revised Feb 2021.
    4. Melek AKSU & Şakir SAKARYA, 2018. "Pricing of Covered Warrants: An Analysis on Borsa İstanbul," Sosyoekonomi Journal, Sosyoekonomi Society.
    5. Jean-Philippe Aguilar & Cyril Coste & Jan Korbel, 2016. "Non-Gaussian analytic option pricing: a closed formula for the L\'evy-stable model," Papers 1609.00987, arXiv.org, revised Nov 2017.
    6. Nuugulu, Samuel M & Gideon, Frednard & Patidar, Kailash C, 2021. "A robust numerical scheme for a time-fractional Black-Scholes partial differential equation describing stock exchange dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    8. Jean-Philippe Aguilar, 2017. "A series representation for the Black-Scholes formula," Papers 1710.01141, arXiv.org, revised Oct 2017.
    9. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    10. Jean-Philippe Aguilar & Cyril Coste & Jan Korbel, 2017. "Series representation of the pricing formula for the European option driven by space-time fractional diffusion," Papers 1712.04990, arXiv.org, revised Oct 2018.
    11. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    12. Alghalith, Moawia, 2020. "Pricing options under simultaneous stochastic volatility and jumps: A simple closed-form formula without numerical/computational methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. Juan M. Romero & Ilse B. Zubieta-Mart'inez, 2016. "Relativistic Quantum Finance," Papers 1604.01447, arXiv.org.
    14. Jean-Philippe Aguilar & Cyril Coste & Hagen Kleinert & Jan Korbel, 2016. "Regularization and analytic option pricing under $\alpha$-stable distribution of arbitrary asymmetry," Papers 1611.04320, arXiv.org, revised Nov 2016.
    15. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Concept of dynamic memory in economics," Papers 1712.09088, arXiv.org.

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