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Pricing of shout option in uncertain financial market

Author

Listed:
  • Haoxuan Li

    (University of International Business and Economics)

  • Xiangfeng Yang

    (University of International Business and Economics)

  • Yaodong Ni

    (University of International Business and Economics)

Abstract

The shout option allows the investors to make "shouts" to the seller throughout the option’s duration. The investors’ payoff is higher between the intrinsic value at shout time and the intrinsic value at the maturity time. Previous shout option pricing is in the framework of probability theory. However, some unexpected events in real life can make the frequency deviate from the estimated distribution function, in which case we should use the uncertainty theory. This study investigates shout option pricing problems under uncertainty theory. It also derives pricing formulas for shout-call and shout-put options. Additionally, we design a numerical algorithm to compute the price of the shout options. Finally, this study applies the concept of the shout option to Microsoft’s stock data and examines the relationship between the option price and crucial parameters.

Suggested Citation

  • Haoxuan Li & Xiangfeng Yang & Yaodong Ni, 2024. "Pricing of shout option in uncertain financial market," Fuzzy Optimization and Decision Making, Springer, vol. 23(3), pages 449-467, September.
    • Handle: RePEc:spr:fuzodm:v:23:y:2024:i:3:d:10.1007_s10700-024-09428-8
    DOI: 10.1007/s10700-024-09428-8
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    References listed on IDEAS

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    1. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    2. 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.
    3. Yu, Yongjiu & Yang, Xiangfeng & Lei, Qing, 2022. "Pricing of equity swaps in uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Min Dai & Yue Kuen Kwok & Lixin Wu, 2004. "Optimal Shouting Policies Of Options With Strike Reset Right," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 383-401, July.
    5. Windcliff, H. & Forsyth, P. A. & Vetzal, K. R., 2001. "Valuation of segregated funds: shout options with maturity extensions," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 1-21, August.
    6. Xiangfeng Yang & Hua Ke, 2023. "Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 447-462, September.
    7. 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.
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    Cited by:

    1. Lifen Jia & Linya Zhang & Wei Chen, 2024. "China’s carbon emission allowance prices forecasting and option designing in uncertain environment," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 539-560, December.

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