G-布朗运动环境下可转换债券定价及实证分析  

Pricing and empirical analysis of convertible bond in the G-Brownian motion environment

作　　者：呼苗 薛红[1] 刘欣 HU Miao;XUE Hong;LIU Xin(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《西安工程大学学报》2020年第5期121-127,共7页Journal of Xi’an Polytechnic University

基　　金：国家自然科学基金(11601410);陕西省自然科学基础研究计划项目(2016JM1031);中国博士后科学基金(2017M613169)。

摘　　要：针对传统Black-Scholes模型中波动率为常数的假设与实际金融市场不符合的问题,利用G-布朗运动刻画股票价格的波动,建立金融市场数学模型。采用滑动窗口法估计上、下方差,利用G-布朗运动的相关理论及定义模拟标的资产价格,结合蒙特卡洛方法模拟得到可转换债券内嵌看涨期权的价格,进一步对可转换债券进行定价。通过长证转债交易数据进行实证分析,并与传统Black-Scholes模型定价结果进行对比,实证结果表明:G-布朗运动环境下的金融市场模型比传统Black-Scholes模型更符合金融市场的变化。To the inconformity that the assumption of constant volatility in the traditional Black-Scholes model is not consistent with the real financial market,the G-Brownian motion was used to describe the changes of the stock price and establish the financial market mathematical model.The sliding window method was used to estimate the upper and lower variance,the relevant theories of G-Brownian motion and the definition were used to simulate the underlying asset price.The Monte Carlo method was used to simulate the price of the embedded call option of the convertible bond,and the convertible bond is further priced.The empirical analysis was made through the data of Changzheng convertible bond transactions,and compared with the pricing results of the traditional Black-Scholes model.The results show that the financial market model in the G-Brownian motion environment is more adapted to the real financial market than the traditional Black-Scholes model.

关 键 词：G-布朗运动 可转换债券 BLACK-SCHOLES模型 数值模拟 蒙特卡洛 实证分析 

分 类 号：F830[经济管理—金融学] O211[理学—概率论与数理统计]