混合分数布朗运动下欧式期权模糊定价研究

doi:10.12005/orms.2022.0233

运筹与管理 ›› 2022, Vol. 31 ›› Issue (7): 173-178.DOI: 10.12005/orms.2022.0233

混合分数布朗运动下欧式期权模糊定价研究

林先伟, 秦学志, 尚勤

大连理工大学经济管理学院,辽宁大连 116024

收稿日期:2020-09-08 发布日期:2022-08-17
作者简介:林先伟(1993-),男,安徽六安人,博士研究生,研究方向:金融工程;秦学志(1965-),男,辽宁大连人,博士,教授,博士生导师,研究方向:金融工程、风险管理。
基金资助:
国家自然科学基金资助项目(71471026,71871040);国家自然科学基金重点项目(71731003);国家社科基金重大项目(18ZDA095);国家社科基金资助项目(19BJY228);辽宁省“兴辽英才计划”哲学社会科学领军人才项目(XLYC1804005);辽宁省社会科学规划基金(L16BGL012)

Fuzzy Pricing of European option Based on Mixed Fractional Brownian Motion

LIN Xian-wei, QIN Xue-zhi, SHANG Qin

School of Economics and Management, Dalian University of Technology, Dalian 116024, China

Received:2020-09-08 Published:2022-08-17

摘要/Abstract

摘要： 本文采用混合分数布朗运动来刻画标的股票价格的动态变化,以此体现金融市场的长记忆性特征。在混合分数Black-Scholes模型的基础上, 基于标的股票价格、无风险利率和波动率均是模糊数的假定下,构建了欧式期权模糊定价模型。其次,分析了金融市场长记忆性的度量指标 Hurst指数H对欧式期权模糊定价模型的影响。最后,数值实验表明:考虑长记忆性特征得到的欧式期权模糊定价模型更符合实际。

关键词: 欧式期权, 混合分数布朗运动, 模糊数, 期权定价

Abstract: In this paper, the mixed fractional Brownian motion is used to describe the dynamic change of the underlying stock price, so as to capture the long-term memory property of the financial market. On the basis of mixed fractional Black-Scholes model, assuming that the underlying stock price, risk-free interest rate and volatility are all fuzzy numbers, a fuzzy pricing model of European options based on mixed fractional Brownian motion is established. Secondly, the influence of Hurst index H, a measure of long-term memory in financial market, on European option pricing is analyzed. Finally, the numerical experimental results show that the fuzzy pricing model of European options based on long memory is more practical.

Key words: european option, mixed fractional brownian motion, fuzzy numbers, option pricing

中图分类号:

F830.9

林先伟, 秦学志, 尚勤. 混合分数布朗运动下欧式期权模糊定价研究[J]. 运筹与管理, 2022, 31(7): 173-178.

LIN Xian-wei, QIN Xue-zhi, SHANG Qin. Fuzzy Pricing of European option Based on Mixed Fractional Brownian Motion[J]. Operations Research and Management Science, 2022, 31(7): 173-178.

参考文献

[1] Zadeh L A. Fuzzy sets. Information and Control, 1965, 8(3): 338-353.
[2] Wu H C. Pricing european options based on the fuzzy pattern of black-scholes formula. Computers & Operations Research, 2004, 31(7): 1069-1081.
[3] Zhang W G, Xiao W L, Kong W T, et al. Fuzzy pricing of geometric asian options and its algorithm. Applied Soft Computing, 2015, 28(1): 360-367.
[4] Qin X Z, Lin, X W, Shang Q. Fuzzy pricing of binary option based on the long memory property of financial markets. Journal of Intelligent & Fuzzy Systems. 2020, 38: 1-12.
[5] 马勇, 张卫国,刘勇军,等.模糊随机环境中的欧式障碍期权定价.系统工程学报,2012,27(5):641-647.
[6] Li H, Ware A, Di L, et al. The application of nonlinear fuzzy parameters PDE method in pricing and hedging european options. Fuzzy Sets and Systems, 2018, 331: 14-25
[7] Lu Z, Yan H, Zhu Y. European option pricing model based on uncertain fractional differential equation. Fuzzy Optimization and Decision Making, 2018. 1-19.
[8] 谭政勋, 张欠.中国股票市场的长期记忆性与趋势预测研究.统计研究,2016,33(10):57-66.
[9] 余立威, 陈涛.股票市场的长记忆及其动态结构.数理统计与管理,2017,36(6):1106-1118.
[10] Zheng M, Liu R, Li Y. Long memory in financial markets: a heterogeneous agent model perspective. International Review of Financial Analysis, 2018, 12: 22-33.
[11] Peters E E. Fractal market analysis: applying chaos theory to investment and economics. Complexity, risk, and financial markets. J. Wiley, 1994. 191-203.
[12] 李大夜.基于分形方法的金融市场长记忆性研究.北京:对外经济贸易大学,2017.
[13] Shiryaev A N. On arbitrage and replication for fractal models. Technical report, MaPhySto, 1998. 11-19.
[14] Cheridito P. Mixed fractional Brownian motion. Bernoulli, 2001, 7(6): 913-934.
[15] Xiao W L, Zhang W G, Zhang X, et al. Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm. Physica A Statistical Mechanics & Its Applications, 2012, 391(24): 6418-6431.
[16] Sun L. Pricing currency options in the mixed fractional brownian motion. Physica A Statistical Mechanics & Its Applications, 2013, 392(16): 3441-3458.
[17] Rao B L S P. Pricing geometric asian power options under mixed fractional brownian motion environment. Physica A Statistical Mechanics & Its Applications, 2016, 446: 92-99.
[18] Ahmadian D, Ballestra L V. Pricing geometric asian rainbow options under the mixed fractional brownian motion. Physica A: Statistical Mechanics and its Applications, 2020. 555-567.
[19] Serinaldi F. Use and misuse of some hurst parameter estimators applied to stationary and non-stationary financial time series. Physica A, 2010, 389(14): 2770-278.

混合分数布朗运动下欧式期权模糊定价研究

Fuzzy Pricing of European option Based on Mixed Fractional Brownian Motion

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