股票价格运行的幂律特征及幂律跳跃扩散模型

Stock pricing model:Jump diffusion model of power law

在Merton提出的跳跃扩散模型的逻辑框架之下,完成了两方面的修正工作:将计数过程由Poisson过程修正为带有幂律性质的更新过程,同时,赋予股票价格运动过程发生跳跃的时间和幅度以幂律分布特征.通过实证研究表明,修正后可以更加准确地描述股票价格的运动过程,同时得到具有尖峰胖尾的收益率分布和波动聚集性.以此为基础可以更加准确地为期权等金融衍生品进行定价,同时也为金融风险管理提供了有效工具.

Based on the Merton＇s jump diffusion model,two amendments are carried out.Firstly,the counting process（Poisson process） will be amended by the renewal process with power-law nature.Secondly,the magnitude of the jump has also been given the characteristics of power-law nature.By empirical research,it is found that the model could accurately describe the process of the stock price movement,and get a yield with fat-tailed distribution and volatility clustering.As a basis,the model can be used to more accurately price financial derivatives products such as options,and also provide effective tools in financial risk management.