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

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.