基于间隔概率优化的多参跳跃扩散模型研究及应用

发布时间：2018-03-16 10:28

本文选题：跳跃间隔　切入点：多参指数分布　出处：《云南财经大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,跳跃扩散模型在实证研究中取得显著效果,然而研究大多针对跳跃扩散模型的跳跃间隔和跳跃幅度进行概率分布假设,鲜有从统计角度分析跳跃特征的实际分布情况。已有研究中,跳跃间隔一般假设为指数分布,也有少数学者利用幂律分布分析跳跃间隔特征。基于跳跃间隔服从指数分布的假设,跳跃发生次数将呈泊松过程。然而,实证研究也发现,指数分布极大地低估了长间隔跳跃的概率。相较于指数分布,利用幂律分布描述跳跃间隔特征可以更好地捕捉价格跳跃的“时变性”和“厚尾性”,但同时,也低估了短间隔的跳跃发生概率。整体而言,指数分布和幂律分布在跳跃间隔描述中各有优劣。基于上述问题,本文立足跳跃与波动理论,引入多参指数分布刻画跳跃间隔特征,试图给出最合适的跳跃间隔概率分布,并构建多参跳跃扩散模型。首先,本文总结了资产价格跳跃间隔特征,得到时变性、递减性、骤降性和厚尾性四个性质。其次,针对四种跳跃间隔性质,利用多参指数分布描述跳跃间隔特征,并构建多参跳跃扩散模型。此外,结合指数分布、幂律分布和多参指数分布进行跳跃间隔特征的实证分析,并对比一般跳跃扩散模型和多参跳跃扩散模型的资产定价精度。结果显示,多参指数分布相对于指数分布和幂律分布能更好地描述跳跃扩散时变性、递减性、骤降性和厚尾性四个性质;多参跳跃扩散模型具有高于一般跳跃扩散模型的定价精度。最后,根据实证结果,建议跳跃扩散模型中使用多参指数分布代替幂律分布或指数分布作为跳跃间隔的概率分布。
[Abstract]:In recent years, the jump diffusion model has achieved remarkable results in empirical research. However, most of the studies are based on the hopping interval and the jump amplitude of the jump diffusion model for the probability distribution hypothesis. It is rare to analyze the actual distribution of jump characteristics from a statistical point of view. In previous studies, the jump interval is generally assumed to be exponential distribution. There are also a few scholars using power law distribution to analyze the characteristics of jump interval. Based on the assumption of exponential distribution of jump-spacer clothing, the number of jumps will be Poisson process. However, empirical research also found that, The exponential distribution greatly underestimates the probability of the long jump. Compared with the exponential distribution, the power law distribution can better capture the "time-varying" and "thick tail" of the price jump, but at the same time, the power law distribution can better capture the "time-varying" and "thick tail" of the price jump. On the whole, exponential distribution and power law distribution have advantages and disadvantages in the description of jump interval. Based on the above problems, this paper bases on the theory of jump and fluctuation. The multiparameter exponential distribution is introduced to characterize the jump interval characteristics, and the most suitable jump interval probability distribution is proposed, and the multi-parameter jump diffusion model is constructed. Firstly, the characteristics of the jump interval in asset prices are summarized, and the time-varying and decreasing properties are obtained. There are four properties of sudden drop and thick tail. Secondly, for the four properties of jump interval, the multiparameter exponential distribution is used to describe the characteristics of jump interval, and a multi-parameter jump diffusion model is constructed. In addition, the exponential distribution is combined with the exponential distribution. The power law distribution and multi-parameter exponential distribution are used to analyze the characteristics of jump interval, and the asset pricing accuracy of general jump diffusion model and multi-parameter jump diffusion model is compared. Compared with exponential distribution and power law distribution, the multiparameter exponential distribution can better describe the four properties of jump diffusion time variability, decrement, sudden drop and thick tail, and the multiparameter jump diffusion model has higher pricing accuracy than the general jump diffusion model. Based on the empirical results, it is suggested that the multiparameter exponential distribution be used in the jump diffusion model instead of the power law distribution or exponential distribution as the probability distribution of the jump interval.
【学位授予单位】：云南财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9

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