基于混合次分数跳过程的亚式期权模糊定价

doi:10.13804/j.cnki.2095-6991.2024.01.003

	基于混合次分数跳过程的亚式期权模糊定价
其他题名	Fuzzy Pricing of Asian Option Based on Sub-mixed Fractional Brownian Motion with Jump
	庞秋月; 汪育兵
	2024-01-10
发表期刊	兰州文理学院学报(自然科学版)
卷号	38 期号:01 页码:9-16
摘要	考虑到金融资产价格的长记忆性及跳跃现象，基于混合次分数布朗运动和泊松过程，建立了几何亚式期权定价模型；进一步考虑金融市场模糊性，引入模糊理论得到模糊定价模型.首先，得到混合次分数跳过程■公式及其股价所满足随机微分方程的解析解；其次，运用风险中性原理给出几何亚式期权的定价公式；然后，运用模糊理论构建了几何亚式模糊期权定价模型；最后，数值模拟分析了置信度和Hurst指数对模糊价格的影响，并将本文所建立模型与经典BS模型进行对比.结果表明，在相应的置信度下模糊定价模型能够给出较为合理的价格区间，有助于金融投资者的决策，从而验证了模型的合理性和实用性.
其他摘要	Considering the long memory of financial asset price and its jumping phenomenon,a geometric Asian option pricing model is established,which is based on sub-mixed fractional Brownian motion and Poisson process.Further considering the fuzziness of financial market,the fuzzy pricing model is obtained by introducing fuzzy theory.Firstly,the sub-mixed frac-tional Itô formula with jump and the analytical solution of stochastic differential equation sa-tisfied by stock price are obtained.Secondly,the closed pricing formula of geometric Asian option is given under the principle of risk neutrality.Then,a geometric Asian fuzzy option pricing model is constructed by using fuzzy theory.Finally,the influence of confidence and Hurst index on fuzzy price is analyzed by numerical simulation,and the model established in this paper is compared with the classic BS model.The results show that the fuzzy pricing model can give a reasonable price range under the corresponding confidence,which is helpful for financial investors to make decisions,thus verifying the rationality and practicability of the model.
关键词	混合次分数跳过程风险中性原理几何亚式期权模糊理论
DOI	10.13804/j.cnki.2095-6991.2024.01.003
URL	查看原文
ISSN	2095-6991
语种	中文
原始文献类型	学术期刊
中图分类号	F830;F224
CN号	62-1212/N
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/35526
专题	统计与数据科学学院
作者单位	兰州财经大学统计与数据科学学院
第一作者单位	统计与数据科学学院
推荐引用方式 GB/T 7714	庞秋月,汪育兵. 基于混合次分数跳过程的亚式期权模糊定价[J]. 兰州文理学院学报(自然科学版),2024,38(01):9-16.
APA	庞秋月,&汪育兵.(2024).基于混合次分数跳过程的亚式期权模糊定价.兰州文理学院学报(自然科学版),38(01),9-16.
MLA	庞秋月,et al."基于混合次分数跳过程的亚式期权模糊定价".兰州文理学院学报(自然科学版) 38.01(2024):9-16.