双分数随机波动率下可转换债券定价及实证分析  

Convertible bond pricing with stochastic volatility in bi-fractional Brownian motion environment and empirical analysis

作　　者：薛红[1] 张娟 王菩 XUE Hong;ZHANG Juan;WANG Pu(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：《纺织高校基础科学学报》2023年第1期94-100,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11871056)。

摘　　要：综合考虑资产价格收益率序列增量非平稳和非独立及波动率的随机性,建立双分数随机波动率下资产价格数学模型,研究可转换债券的定价。采用极大似然估计方法得到模型中参数,根据蒙特卡洛数值模拟方法,计算可转换债券价格。通过国投转债数据进行实证分析,并与其他模型对比。研究结果表明,双分数随机波动率下的可转换债券定价模型更符合实际金融市场。Considering the non-stationary and non-independent increment and stochastic volatility rate of asset price return rate series, the pricing model of convertible bond is established under the bi-fractional stochastic volatility rate, and the parameters in the model are obtained using maximum likelihood estimation method, according to Monte-Carlo numerical simulation method, the price of convertible bond is calculated. The data of Guotou convertible bond is used for empirical analysis, and the comparative analysis is made with other models. The research results show that the pricing model of convertible bond under the bi-fractional stochastic volatility rate is more adapted to the actual financial market.

关 键 词：可转换债券定价 双分数布朗运动 随机波动率 蒙特卡洛模拟 

分 类 号：O211[理学—概率论与数理统计] F830[理学—数学]