EGARCH模型参数的拟蒙特卡洛估计方法及其在股票指数上的应用

发布时间：2018-03-16 22:25

本文选题：EGARCH模型　切入点：拟随机数　出处：《上海大学》2012年硕士论文　论文类型：学位论文

【摘要】：波动性(Volatility)是证券市场的一个重要特性，是数量经济学和统计科学面临的最重要问题之一，与金融市场的功能、稳定性密切相关，在金融资产定价和资产配中处于十分总要的位置，是体现资本市场价格行为、质量和效率的有效指标之一。对于一个发展比较成熟的资本市场而言，应该有比较适度的微小波动，而频繁和波幅过大的震荡不仅对投资者做出正确的投资组合策略不利，也会危害整个金融市场的健康、稳定和发展，甚至可能诱发全球性金融危机，所以证券市场的收益率波动特征以及影响因素备受各研究学者的关注。2010年我国推出沪深了300股指期货，股票市场波动问题变得更加复杂。本文就是在这样的背景下开始对我国沪深300股票指数的研究，在研究方法上由于股票指数序列存在自相关与异方差的问题，不能再应用传统意义上的收益率和风险度量方法，因此需要基于ADF的单位根检验(Unit Root Test)、协整检验，最终通过建立EGARCH模型来反映股票市场带有非对称性的波动特性。本文系统阐述了ARCH类模型的基本理论，分析了ARCH类模型的基本性质特征，并着重探讨了这类模型的参数估计方法。极大似然估计方法是现阶段最广泛使用的参数估计方法。虽然有学者提出了BHHH算法和广义矩方法等一些较为先进的算法来得到模型参数的分布，并以此获取模型参数更多的信息。然而在实际运算中这类算法常遇到中间数据震荡从而导致算法整体失效的问题。也有学者选择了使用马尔科夫链Monte Carlo(MCMC)方法来计算ARCH类模型的后验分布，然而该方法需要采取如Griddy-Gibbs，Metropolis-Hastings等较为复杂的抽样方法，使用起来很不方便。国内有学者提出了一种估计GARCH(1,1)模型参数的简便有效的常规Monte Carlo方法，本文在该工作基础上，选择Halton序列替代原方法中的均匀分布作为参数的先验分布，并将该方法从GARCH（1,1）模型推广到EGARCH模型。最终表明了这种方法在估计EGARCH模型参数时的有效性。本文主要从以下几个方面进行研究： 1)系统地阐述了自回归条件异方差回归模型族的产生背景，统计意义，以及当前国内外的研究现状与发展水平等。并详细介绍了本文使用的常规MonteCarlo方法的理论基础——Bayes推断理论。 2)详细阐述了拟蒙特卡洛方法的理论部分，并通过MATLAB软件设计实验，对比分析了拟随机数与伪随机数的区别，通过实验结果来直观地呈现本文使用拟随机数代替伪随机数的原因——拟随机数用有的更好的统计特性。 3)结合我国的股票市场，在实证分析中通过对沪深300指数时间序列数据的分析，建立EGARCH模型，，并给出了该模型参数的具体的常规拟蒙特卡洛估计方法，通过与最大似然估计方法对比，证明了该方法的有效性。
[Abstract]:Volatility volatility is an important characteristic of securities market. It is one of the most important problems faced by quantitative economics and statistical science. It is closely related to the function and stability of financial market. It is one of the most effective indicators of capital market price behavior, quality and efficiency in financial asset pricing and asset allocation. There should be moderate small fluctuations, and frequent and excessive volatility is not only bad for investors to make the right portfolio strategy, but also endangers the health, stability and development of the entire financial market. It may even lead to a global financial crisis, so the volatility characteristics of the yield and the influencing factors of the securities market have attracted the attention of various researchers. In 2010, China launched the Shanghai and Shenzhen 300 stock index futures. The volatility of stock market has become more complicated. This paper begins to study the stock index of Shanghai and Shenzhen 300 stock index in China under this background. In the research method, because of the problem of autocorrelation and heteroscedasticity in stock index sequence, The traditional methods of yield and risk measurement can no longer be applied, so the unit root test based on ADF and the cointegration test are needed. Finally, the EGARCH model is established to reflect the asymmetric volatility of the stock market. In this paper, the basic theory of ARCH class model is expounded, and the basic properties of ARCH class model are analyzed. The maximum likelihood estimation method is the most widely used parameter estimation method at present. Although some scholars have put forward some advanced algorithms such as BHHH algorithm and generalized moment method, etc. To get the distribution of model parameters, And get more information about the model parameters. However, in the actual operation, this kind of algorithms often encounter the problem of intermediate data oscillation, which leads to the overall failure of the algorithm. Some scholars have also chosen to use the Markov chain Monte method to calculate the problem. The posterior distribution of ARCH model is calculated. However, this method needs more complicated sampling methods such as Griddy-Gibbsl Metropolis-Hastings, which is very inconvenient to use. Some domestic scholars have proposed a simple and effective conventional Monte Carlo method to estimate the parameters of the GARCH1) model. The Halton sequence is used to replace the uniform distribution in the original method as the prior distribution of the parameters, and the method is extended from the Garch 1 / 1) model to the EGARCH model. Finally, the effectiveness of this method in estimating the parameters of the EGARCH model is demonstrated. This article mainly carries on the research from the following several aspects:. 1) the background of autoregressive conditional heteroscedasticity regression model family, its statistical significance, the current research status and development level at home and abroad, etc., and the theoretical basis of the conventional MonteCarlo method used in this paper, the Bayesian inference theory, are introduced in detail. 2) the theoretical part of quasi Monte Carlo method is expounded in detail, and the difference between pseudo random number and pseudorandom number is compared and analyzed by MATLAB software design experiment. The experimental results show the reason why pseudorandom numbers are replaced by pseudorandom numbers in this paper, which has better statistical characteristics. 3) combining the stock market of our country, through the analysis of the time series data of CSI 300 index, the EGARCH model is established, and the concrete method of quasi Monte Carlo estimation of the parameters of this model is given. The effectiveness of the proposed method is proved by comparison with the maximum likelihood estimation method.
【学位授予单位】：上海大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.51;F224

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