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Simple Formulas for Pricing and Hedging European Options in the Finite Moment Log-Stable Model

Author

Listed:
  • Jean-Philippe Aguilar

    (BRED Banque Populaire, Modeling Department, 18 quai de la Râpée, 75012 Paris, France)

  • Jan Korbel

    (Section for the Science of Complex Systems, Center for Medical Statistics, Informatics, and Intelligent Systems (CeMSIIS), Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria
    Complexity Science Hub Vienna, Josefstädterstrasse 39, 1080 Vienna, Austria
    Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, 11519 Prague, Czech Republic)

Abstract

We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy-stable models with maximal negative asymmetry. Particular cases, efficiency testing, and some qualitative features of the model are also discussed.

Suggested Citation

  • Jean-Philippe Aguilar & Jan Korbel, 2019. "Simple Formulas for Pricing and Hedging European Options in the Finite Moment Log-Stable Model," Risks, MDPI, vol. 7(2), pages 1-14, April.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:36-:d:219656
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    References listed on IDEAS

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    1. repec:bla:jfinan:v:58:y:2003:i:2:p:753-778 is not listed on IDEAS
    2. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    3. Jin-Chuan Duan & Ivilina Popova & Peter Ritchken, 2002. "Option pricing under regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 116-132.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Jean-Philippe Aguilar & Jan Korbel, 2018. "Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications," Papers 1802.09864, arXiv.org.
    6. Kleinert, H. & Korbel, J., 2016. "Option pricing beyond Black–Scholes based on double-fractional diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 200-214.
    7. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    8. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    9. 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.
    10. Sun, Lin, 2013. "Pricing currency options in the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3441-3458.
    11. 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.
    12. Laurent E. Calvet & Adlai Fisher, 2008. "Multifractal Volatility: Theory, Forecasting and Pricing," Post-Print hal-00671877, HAL.
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    Citations

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    Cited by:

    1. Jean-Philippe Aguilar, 2021. "The value of power-related options under spectrally negative Lévy processes," Review of Derivatives Research, Springer, vol. 24(2), pages 173-196, July.
    2. Pedro Febrer & João Guerra, 2021. "Residue Sum Formula for Pricing Options under the Variance Gamma Model," Mathematics, MDPI, vol. 9(10), pages 1-29, May.
    3. Jean-Philippe Aguilar, 2019. "The value of power-related options under spectrally negative L\'evy processes," Papers 1910.07971, arXiv.org, revised Jan 2021.
    4. 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.

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