基于FMLS模型的欧式期权定价与对冲策略
European Option Pricing and Hedging Strategy Based on the Finite Moment Log-Stable Process
DOI: 10.12677/AAM.2019.88174, PDF,    科研立项经费支持
作者: 范聪银：贵州商学院财政金融学院，贵州 贵阳；车嘉懿：贵州商学院管理学院，贵州 贵阳
关键词: 有限矩对数稳态过程；期权定价；方差最优对冲；隐含波动率；Finite Moment Log-Stable Process； Option Pricing； Variance Optimal Hedging； Implied Volatility
摘要: 实证研究表明美国市场上股票的对数收益并不服从正态分布而是服从非对称的分布。为此，我们基于有限矩对数稳态过程(FMLS)来研究欧式期权的定价与方差最优对冲策略。首先，利用卷积定价原理推导FMLS框架下欧式期权的定价公式，并设计相应的数学实验对该公式进行检验；其次，根据期权对冲的基本原理，本文通过求解一个非线性优化问题得到FMLS框架下欧式期权的方差最优对冲策略；最后，为了能够直观地看到FMLS模型对风险的捕捉能力，本文还进行了相应的数值模拟并同Black-Scholes (BS)模型下的结果进行比较。
Abstract: The empirical test suggests that the log-return series of stock price in US market reject the normal distribution and admit instead a subclass of the asymmetric distribution. Therefore, the European option pricing and variance optimal hedging strategy are investigated based on the finite moment log-stable process (FMLS) in this paper. Firstly, the pricing formula of European option is derived by using the principle of convolution pricing, and we design a mathematical experiment to test this formula. Secondly, according to the principle of option hedging, the variance optimal hedging of the European option obtained under the FMLS frame by solving a nonlinear optimization problem. Finally, the numerical results are simulated and we compare the results between the FMLS and Black-Scholes (BS) models to observe the ability of capture risk of FMLS model.
文章引用：范聪银, 车嘉懿. 基于FMLS模型的欧式期权定价与对冲策略[J]. 应用数学进展, 2019, 8(8): 1487-1499. https://doi.org/10.12677/AAM.2019.88174

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