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N-Fold Compound Option Fuzzy Pricing Based on the Fractional Brownian Motion

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Abstract

In this paper, we present a new pricing method on N-fold compound option by adopting the theory of fuzzy sets into a fractional stochastic financial model. Considering the characteristics of correlations and kurtosis of returns in the long run, we employ the fractional Brownian motion to model the dynamic price of underlying assets. Then, a trapezoidal fuzzy stochastic process is employed to depict the fuzziness of underlying asset price. Involving the decision-maker’s subjective judgment, the mean value with the possibility–necessity weight and pessimistic–optimistic index is expressed. Further, the formulas of N-fold compound option price are derived by martingale method. Moreover, the valuation and properties of the formulas are analyzed under some reasonable assumptions. In the end, some numerical examples are provided to support our theoretical results and illustrate the mean of N-fold compound option pricing in fuzzy and fractional environments.

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Acknowledgements

The work was supported by the Scientific Research Foundation of Chengdu University of Information Technology Nos. KYTZ202197, KYTZ202196. The work was also supported by the Natural Science Foundation of Gansu Province No. 21JR7RP859. The corresponding author of this paper is Peimin Chen with email address: pmchen@sbs.edu.cn.

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Authors and Affiliations

  1. The School of Statistics, Chengdu University of Information Technology, Chengdu, 610110, People’s Republic of China

    Pingping Zhao & Tong Wang

  2. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Kaili Xiang

  3. Shanghai Business School, Shanghai, 200235, People’s Republic of China

    Peimin Chen

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  1. Pingping Zhao
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  2. Tong Wang
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  3. Kaili Xiang
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  4. Peimin Chen
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Correspondence to Peimin Chen.

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Zhao, P., Wang, T., Xiang, K. et al. N-Fold Compound Option Fuzzy Pricing Based on the Fractional Brownian Motion. Int. J. Fuzzy Syst. 24, 2767–2782 (2022). https://doi.org/10.1007/s40815-022-01283-2

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  • DOI: https://doi.org/10.1007/s40815-022-01283-2

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