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Fuzzy simulation of European option pricing using sub-fractional Brownian motion

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  • Bian, Liu
  • Li, Zhi

Abstract

On the basis of the sub-fractional Black-Scholes model, considering that the financial market is uncertain with randomness and fuzziness, we used stochastic analysis, fractal theory and fuzzy set theory to construct European option pricing model based on the long-term memory property of the financial market in an uncertain environment. Afterwards the influence of Hurst index H, a measure of long-term memory in financial market, on European option pricing is analyzed. Finally, the rationality and feasibility of the pricing model are demonstrated by numerical experiment. The obtained results show that the European options pricing model with long-term memory property is more suitable for financial markets under uncertain environment.

Suggested Citation

  • Bian, Liu & Li, Zhi, 2021. "Fuzzy simulation of European option pricing using sub-fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921007967
    DOI: 10.1016/j.chaos.2021.111442
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    References listed on IDEAS

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    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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    Cited by:

    1. Xinyue Wei & Cuilian You & Yujie Zhang, 2023. "European Option Pricing Under Fuzzy CEV Model," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 415-432, February.
    2. Ma, Pengcheng & Najafi, Alireza & Gomez-Aguilar, J.F., 2024. "Sub mixed fractional Brownian motion and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    3. Xianfei Hui & Baiqing Sun & Hui Jiang & Yan Zhou, 2022. "Modeling dynamic volatility under uncertain environment with fuzziness and randomness," Papers 2204.12657, arXiv.org, revised Oct 2022.
    4. Hersugondo Hersugondo & Endang Tri Widyarti & Di Asih I Maruddani & Trimono Trimono, 2022. "ASEAN-5 Stock Price Index Valuation after COVID-19 Outbreak through GBM-MCS and VaR-SDPP Methods," IJFS, MDPI, vol. 10(4), pages 1-19, November.
    5. Wang, Song, 2024. "Pricing European call options with interval-valued volatility and interest rate," Applied Mathematics and Computation, Elsevier, vol. 474(C).

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