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Pricing Asian options under the mixed fractional Brownian motion with jumps

Author

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  • Shokrollahi, F.
  • Ahmadian, D.
  • Ballestra, L.V.

Abstract

The mixed fractional Brownian motion (mfBm) has gained popularity in finance because it can effectively model long-range dependence, self-similarity, and is arbitrage-free. This paper focuses on mfBm with jumps modeled by the Poisson process and derives an analytical formula for valuing geometric Asian options. Additionally, approximate closed-form solutions for pricing arithmetic Asian options and arithmetic Asian power options are obtained. Numerical examples are provided to demonstrate the accuracy of these formulas, which rely on a convenient approximation of the option strike price. The proposed approximation demonstrates significantly higher computational efficiency compared to Monte Carlo simulation.

Suggested Citation

  • Shokrollahi, F. & Ahmadian, D. & Ballestra, L.V., 2024. "Pricing Asian options under the mixed fractional Brownian motion with jumps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 172-183.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:172-183
    DOI: 10.1016/j.matcom.2024.06.014
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    References listed on IDEAS

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