跳—扩散模型一种新的参数估计方法及应用

发布时间：2018-01-21 02:53

本文关键词： 跳-扩散模型异常值检验参数估计　出处：《北方工业大学》2013年硕士论文　论文类型：学位论文

【摘要】：近年来,金融市场发生了巨大变革,主要是由期权及其它金融衍生品定价模型的不断改进和完善引起的,而金融衍生品定价模型的应用是否成功,很大程度上取决于模型的选择是否合适,模型参数的估计方法是否得当,跳-扩散模型是很重要的一种定价模型,在研究期权定价、利率、汇率的突变方面有其广泛的应用,本文拟对跳-扩散模型的参数估计及检验方面作一些探索性的研究,从而丰富估计方法的多样性,具有一定的实际应用价值。将异常值检验思想应用到跳-扩散模型参数估计的这种新估计方法,较为新颖,计算也比较简便。本文针对跳跃幅度服从正态分布和正、负跳跃幅度服从指数分布这两种跳-扩散模型,首先,将一种新的异常值检验方法应用到跳-扩散模型的参数估计过程中,具体做法是利用异常值检验方法寻找跳跃点,将跳跃过程分离出来,以便分别估计跳跃过程和扩散过程的参数；其次,利用蒙特卡洛模拟考察该估计方法的效果,并讨论估计过程中K值的选择；最后,将本文提出的跳-扩散模型参数估计应用到上证指数和深证综合指数的日收益率序列,以考察收益率的变动行为。模拟分析后,得到相应估计结果,综合t统计量和相对误差两个方面来看,估计的结果较为准确,这也说明该估计方法有其实用性。另外,由于本文所采用的异常值检验方法不依赖于数据的分布,因此对不同的跳-扩散模型具有较好的通用性。本文的实证分析表明用跳-扩散模型对上证指数和深证综合指数的日收益率建模有比较好的效果。
[Abstract]:In recent years, great changes have taken place in the financial market, mainly caused by the continuous improvement and improvement of the pricing models of options and other financial derivatives, and whether the application of the pricing models of financial derivatives is successful. To a great extent, it depends on whether the model is suitable or not, whether the estimation method of model parameters is appropriate or not. The jump-diffusion model is a very important pricing model in the study of option pricing, interest rate. The sudden change of exchange rate has its wide application, this paper intends to do some exploratory research on the parameter estimation and test of hop-diffusion model, so as to enrich the diversity of estimation methods. It has certain practical application value. The new method of estimating the parameters of hop-diffusion model by applying the idea of outliers test is novel and easy to calculate. In this paper, the normal distribution and the positive value of the jump amplitude are studied. There are two kinds of hop-diffusion models with negative jump amplitude distribution. Firstly, a new outliers test method is applied to the parameter estimation of the hop-diffusion model. In order to estimate the parameters of jump process and diffusion process, the method of outlier value test is used to find the jump point and separate the jump process. Secondly, Monte Carlo simulation is used to investigate the effect of this method, and the choice of K value in the estimation process is discussed. Finally, the parameter estimation of hop-diffusion model proposed in this paper is applied to the daily return series of Shanghai Stock Exchange Index and Shenzhen Composite Index to investigate the variation behavior of return rate. After simulation and analysis, the corresponding estimation results are obtained. From the point of view of t statistics and relative error, the estimation results are more accurate, which also shows that the estimation method has its practicability. Because the outlier value checking method adopted in this paper is independent of the distribution of data. The empirical analysis of this paper shows that the Jump Diffusion Model has a good effect on the daily return modeling of Shanghai Stock Exchange Index and Shenzhen Composite Index.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;O212

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