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Fractional Partial Differential Equations Associated with L ê vy Stable Process

Author

Listed:
  • Reem Abdullah Aljedhi

    (Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

  • Adem Kılıçman

    (Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

Abstract

In this study, we first present a time-fractional L e ^ vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L e ^ vy-time fractional diffusion equation of European-style options. Further, we introduce a more general model based on the L e ^ vy-time fractional diffusion equation and review some recent findings associated with risk-neutral free European option pricing.

Suggested Citation

  • Reem Abdullah Aljedhi & Adem Kılıçman, 2020. "Fractional Partial Differential Equations Associated with L ê vy Stable Process," Mathematics, MDPI, vol. 8(4), pages 1-7, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:508-:d:340650
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    References listed on IDEAS

    as
    1. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    2. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
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