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Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications

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  • Jean-Philippe Aguilar
  • Jan Korbel

Abstract

In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from real markets. We focus on estimation of model parameters from the market data and estimation of implied volatility within the space-time fractional option pricing models.

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  • 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.
    • Handle: RePEc:arx:papers:1802.09864
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Nikolaos Roidos & Yuanzhen Shao, 2023. "The fractional porous medium equation on manifolds with conical singularities II," Mathematische Nachrichten, Wiley Blackwell, vol. 296(4), pages 1616-1650, April.

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