基于次分数Black-Scholes模型的欧式期权定价  

European Option Pricing Based on the Subfraction Black-Scholes Model

作　　者：靳晨萱 霍海峰 温鲜 徐东 JIN Chen-xuan;HUO Hai-feng;WEN Xiang;XU Dong(School of Science,Guangxi University of Science and Technology,Liuzhou 541004,China;Houma Branch,Bank of China,Houma 043000,China)

机构地区：[1]广西科技大学理学院,广西柳州541004 [2]中国银行股份有限公司侯马支行,山西侯马043000

出　　处：《南宁师范大学学报（自然科学版）》2021年第3期31-36,共6页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学地区基金科学项目(11961005);广西自然科学基金项目(2020GXNSFAA297196)。

摘　　要：基于次分数Black-Scholes模型,从理论推导和数值计算探讨了欧式期权定价问题.首先,以次分数布朗运动为基础建立次分数Black-Scholes模型,利用伊藤公式得到股票价格变化过程满足的关系式,进一步利用概率方法得出欧式看涨期权价格的显示解.最后,以国电JTB1权证为例,计算理论模型的期权价格,并分别与经典Black-Scholes模型、二叉树模型和实际价格进行比较分析,进而验证模型定价结果的合理性和有效性.Based on the secondary fraction Black-Scholes model,the European option pricing problem is discussed from the theoretical deduction and numerical calculation.First,establishing the subfractional Black-Scholes model of stock price satisfaction based on the subfractional Brownian motion,using the Ito formula to solve the relationship satisfied by the stock price change process,and further using the probabilistic method to obtain the display solution of the European call option price.Finally,taking Guodian JTB1 warrant as an example,the option price of the theoretical model is calculated and analyzed with the classical Black-Scholes model,the binary tree model and the actual price respectively to verify the rationality and effectiveness of the model pricing results.

关 键 词：次分数Black-Scholes模型 次分数伊藤公式 欧式看涨期权 二叉树 

分 类 号：O212.6[理学—概率论与数理统计]