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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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    1. Jagers, Peter & Klebaner, Fima C., 2000. "Population-size-dependent and age-dependent branching processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 235-254, June.
    2. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
    3. Serinaldi, Francesco, 2010. "Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2770-2781.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    5. Mariani, M.C. & Florescu, I. & Beccar Varela, M.P. & Ncheuguim, E., 2010. "Study of memory effects in international market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1653-1664.
    6. Zheng, Min & Liu, Ruipeng & Li, Youwei, 2018. "Long memory in financial markets: A heterogeneous agent model perspective," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 38-51.
    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.
    8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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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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