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Option Pricing and Parameter Estimation for Uncertain Mean-Reverting Currency Model

Author

Listed:
  • Lujun Zhou

    (Guangxi University of Finance and Economics, China-ASEAN Institute of Statistics)

  • Zhenhua He

    (Guangxi University of Finance and Economics, School of Mathematics and Quantitative Economics)

  • Jianmin Liu

    (Guangxi University of Finance and Economics, School of Big Data and Artificial Intelligence)

  • Xiaolan Yin

    (Guangxi University of Finance and Economics, Innovation and Entrepreneurship Academy)

Abstract

Option pricing problem is one of the significant issues in the foreign exchange market, which has attracted the attentions of many researchers. Unlike the classical stochastic theory, we investigate option pricing by an uncertain currency model under the foundation of uncertainty theory. By considering that the domestic interest rate, the foreign interest rate and exchange rate have long-term fluctuations, this paper mainly introduces the uncertain mean-reverting currency model, and conducts the pricing formula of European call options and American call options. Furthermore, the moment methods would be applied to estimating all unknown parameters of the currency model by using Australian Interbank Overnight Cash Rate, US Federal Funds Effective Rate and their Exchange Rate (ExR). Moreover, this paper takes the Goodness-of-Fit Test on whether the moment estimates are acceptable. Finally, the numerical examples and algorithms are used to calculate the option prices and to illustrate the relationship between the two prices and the relationship between prices and their parameters. The appendix justifies our preference for the uncertain currency model over the stochastic one for forex market analysis, based on the latter’s superior fit to empirical data.

Suggested Citation

  • Lujun Zhou & Zhenhua He & Jianmin Liu & Xiaolan Yin, 2025. "Option Pricing and Parameter Estimation for Uncertain Mean-Reverting Currency Model," Computational Economics, Springer;Society for Computational Economics, vol. 66(6), pages 4781-4811, December.
    • Handle: RePEc:kap:compec:v:66:y:2025:i:6:d:10.1007_s10614-025-10872-w
    DOI: 10.1007/s10614-025-10872-w
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    References listed on IDEAS

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    1. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Deng, Jie & Qin, Zhongfeng, 2021. "On Parisian option pricing for uncertain currency model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. 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.
    4. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    6. Tingqing Ye & Baoding Liu, 2022. "Uncertain hypothesis test with application to uncertain regression analysis," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 157-174, June.
    7. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    8. Kai Yao & Zhongfeng Qin, 2021. "Barrier option pricing formulas of an uncertain stock model," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 81-100, March.
    9. Xiaowei Chen & Jing Li & Chen Xiao & Peilin Yang, 2021. "Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 189-208, June.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
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    Cited by:

    1. Zhihan Shi & Yaodong Ni & Xiangfeng Yang, 2026. "Cumulative-Parisian Option Pricing in Uncertainty Theory," Computational Economics, Springer;Society for Computational Economics, vol. 68(2), pages 1659-1684, August.

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