混合次分数布朗运动跳扩散环境下可转债定价研究  

Study on convertible bond pricing model under mixed subfractional Brownian motion jump diffusion environment

作　　者：徐彪 陶祥兴[1] XU Biao;TAO Xiangxing(School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,Zhejiang,China)

机构地区：[1]浙江科技学院理学院,杭州310023

出　　处：《浙江科技学院学报》2023年第1期62-71,共10页Journal of Zhejiang University of Science and Technology

基　　金：国家自然科学基金项目(11771399)。

摘　　要：【目的】为了体现可转债标的资产长记忆性和跳跃性的特点,解决资产收益率增量的不平稳性,提出混合次分数布朗运动跳扩散环境下可转债定价模型。【方法】首先令可转债标的资产的价格变化符合混合次分数布朗运动跳扩散环境;然后利用随机分析理论和随机偏微分方程方法,推导出混合次分数布朗运动跳扩散环境下可转债定价模型,并进一步给出定价模型的参数估计方式;最后运用遗传算法估计参数,选取国内可转债市场的实际数据进行实证分析,结合不同定价模型做对比分析。【结果】本模型对实际价格的拟合效果比传统的布莱克-斯科尔斯模型均方误差平均减少0.34%;通过对遗传算法得到的参数进行定价的拟合效果,比使用历史数据得到的参数进行定价的拟合效果,均方误差平均减少约0.31%。【结论】本模型能在实际市场上为可转债的首日及每日定价决策提供较可靠的理论依据。[Objective] In order to embody the long-memory and jumping characteristics of the asset of convertible bonds and solve the instability of the incremental return on assets, the pricing model of convertible bonds under the mixed subfractional Brownian motion jump diffusion environment was proposed. [Method] To begin with, the price change of the underlying asset of convertible bonds was put in line with the mixed subfractional Brownian motion jump diffusion environment;moreover, the stochastic analysis theory and the stochastic partial differential equation method were applied to deduce the pricing model of convertible bonds under the mixed subfractional Brownian motion jump diffusion environment, and then derive the parameter estimation method of the pricing model;finally, the genetic algorithm was employed to estimate the parameters and the actual data of domestic convertible bond market were selected to empirically and comparatively analyze different pricing models. [Result] The fitting effect of this model on the actual price reduces the mean square error by 0.34%, compared with the traditional Black-Scholes model. The fitting effect of pricing on the parameters obtained by the genetic algorithm reduces the mean square error by approximately 0.31%, compared with the fitting effect of pricing on the parameters obtained by the historical data. [Conclusion] This model can provide a more reliable theoretical basis for first-day pricing and daily pricing strategies of convertible bonds in the real market.

关 键 词：混合次分数布朗运动 可转债 跳扩散 遗传算法 

分 类 号：F224.9[经济管理—国民经济]