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A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion

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  • Ballestra, Luca Vincenzo
  • Pacelli, Graziella
  • Radi, Davide

Abstract

We deal with the problem of pricing barrier options on an underlying described by the mixed fractional Brownian model. To this aim, we consider the initial-boundary value partial differential problem that yields the option price and we derive an integral representation of it in which the integrand functions must be obtained solving Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to solve the integral equations obtained. Numerical simulations reveal that the proposed method is extremely accurate and fast, and performs significantly better than the finite difference method.

Suggested Citation

  • Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 240-248.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:240-248
    DOI: 10.1016/j.chaos.2016.04.008
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    1. Yang, Xiangfeng & Zhang, Zhiqiang & Gao, Xin, 2019. "Asian-barrier option pricing formulas of uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 79-86.
    2. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    3. Wei-Guo Zhang & Zhe Li & Yong-Jun Liu & Yue Zhang, 2021. "Pricing European Option Under Fuzzy Mixed Fractional Brownian Motion Model with Jumps," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 483-515, August.
    4. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    5. Foad Shokrollahi & Davood Ahmadian & Luca Vincenzo Ballestra, 2021. "Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps," Papers 2105.06999, arXiv.org.
    6. Zeng, Yue & Zhang, Yao-jia & Huang, Nan-jing, 2024. "A stochastic fractional differential variational inequality with Lévy jump and its application," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    7. Farshid Mehrdoust & Ali Reza Najafi, 2018. "Pricing European Options under Fractional Black–Scholes Model with a Weak Payoff Function," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 685-706, August.
    8. Marianito R. Rodrigo, 2020. "Pricing of Barrier Options on Underlying Assets with Jump-Diffusion Dynamics: A Mellin Transform Approach," Mathematics, MDPI, vol. 8(8), pages 1-20, August.

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