一种新的股票模型的期权定价公式
Option Pricing Formula for a New Stock Model
DOI: 10.12677/AAM.2018.710142, PDF,  被引量    国家自然科学基金支持
作者: 张元元, 尤翠莲：河北大学数学与信息科学学院，河北 保定
关键词: 模糊过程；Liu过程；模糊微分方程；股票模型；期权定价；Fuzzy Process； Liu Process； Stock Model； Fuzzy Differential Equation； Option Pricing
摘要: 期权定价问题是现代金融的中心内容之一，Black和Scholes假设股票价格的波动符合几何布朗运动，随后在此基础上建立了随机金融数学，但是不确定环境中的不确定因素除了随机性还有模糊性，因此有必要对模糊金融市场进行研究。本文借助可信性理论，讨论了期权中的执行价格满足一扩散过程的情况，得出了该种新的股票模型的期权定价公式。
Abstract: The option pricing problem is one of central contents in modern finance. Black and Scholes assume that the fluctuation of stock price conforms to geometric Brownian motion, and then establishes stochastic financial mathematics on this basis. However, the uncertainties in the uncertain environment are not only random but also fuzzy, so it is necessary to study the fuzzy financial market. Based on the credibility theory, this paper discusses the case that the execution price of an option satisfies a diffusion process, and obtains the option pricing formula of this new stock model.
文章引用：张元元, 尤翠莲. 一种新的股票模型的期权定价公式[J]. 应用数学进展, 2018, 7(10): 1225-1232. https://doi.org/10.12677/AAM.2018.710142

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