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Bermuda option pricing problem modeled by uncertain fractional differential equations and nonparametric estimation analysis

Author

Listed:
  • Jin, Ting
  • Zhang, Ningjuan
  • Dai, Guowei
  • Hu, Tongtong
  • Li, Haoxuan

Abstract

To address the pricing problem of Bermuda options, this paper establishes a mathematical model based on Caputo-type uncertain fractional differential equations (UFDE). By deriving the extremum distribution theorem for UFDE solutions in discrete-time scenarios, explicit pricing formulas for call and put options are obtained. To solve this model, we employ a nonparametric estimation method based on Legendre polynomials for parameter calibration, while simultaneously designing a fractional-order prediction-correction algorithm incorporating Gauss-Chebyshev approximation. Numerical experiments demonstrate that this UFDE model outperforms traditional uncertain differential equations (UDE) and stochastic differential equation (SDE) models in predictive accuracy. Its robustness and ability to capture the volatility smile phenomenon further validate the model’s effectiveness, providing a rigorous theoretical framework and numerical tool for path-dependent derivative pricing.

Suggested Citation

  • Jin, Ting & Zhang, Ningjuan & Dai, Guowei & Hu, Tongtong & Li, Haoxuan, 2026. "Bermuda option pricing problem modeled by uncertain fractional differential equations and nonparametric estimation analysis," Applied Mathematics and Computation, Elsevier, vol. 513(C).
    • Handle: RePEc:eee:apmaco:v:513:y:2026:i:c:s0096300325005168
    DOI: 10.1016/j.amc.2025.129791
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    References listed on IDEAS

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