基于混合正态分布的ARMA-GARCH模型及其VaR风险度量

发布时间：2018-03-29 04:14

本文选题：BaR　切入点：ARMA-GARCH模型　出处：《西北农林科技大学》2012年硕士论文

【摘要】：金融市场发展日新月异，越来越多的人已经或者正在参与其中。然而金融市场的波动也是有目共睹的，举个例子股票的价格起起落落、变化莫测，因此人们在投资时往往存在很大的风险性。风险价值简称VaR(Value at Risk)，VaR方法是目前国际上金融风险管理的主流方法，通过对风险进行分析、测度来尽可能地规避风险。这样看来VaR的度量有很大的现实意义，但能否准确得度量它却是一个值得研究和优化的统计问题。 VaR的定义是，在正常的市场水平和给定置信水平下，一定持有期间内金融资产或投资组合预期未来可能的最大损失。换句话说，正常的市场水平和一定时期内该金融资产或投资组合在给定的概率水平下才会发生或超过VaR值的损失。由定义看出VaR方法与概率统计息息相关，它可以通过计算被量化为一个数字用来表示一定概率水平下某段时期金融资产或投资组合的最大损失。VaR的计算方法很多各有各的优缺点，但都很难使结果非常准确，我们只有通过不断研究尽可能周全得考虑问题减小误差。本文考虑到金融时间序列数据经常出现的尖峰厚尾和异方差特性，，计划针对存在这些特性的金融数据建立基于混合正态分布的ARMA-GARCH(广义条件异方差)模型。首先介绍ARMA-GARCH模型的特性与形式、模型的识别和参数估计等，这一模型是解决具有ARCH效应的金融数据的最佳模型。其次，针对金融数据的尖峰厚尾特性，本文将假定GARCH模型的随机序列服从混合正态分布，因为虽然基于正态分布下GARCH模型也能解决波动率的异方差特性，但它在拟合数据的厚尾性和有偏性时显得不足，而混合正态分布既保留了正态分布的优良特性又能在一定程度上解决尖峰厚尾特性适当的改善正态分布低估风险价值的缺陷。再次，根据VaR模型的定义利用GARCH模型中随机序列基于混合正态分布的风险价值与金融资产收益率的风险价值的函数关系得到研究对象（金融资产或投资组合）的风险价值。最后，选取一组合适的股票数据（深证综指）利用本文研究方法进行实证分析并得出结论证明该方法的优越性。本文设计的这种新方法虽然在组合结构上较显复杂，但考虑问题较周全（尽可能地去减少以往模型中由于一些问题引起的模型误差），经过实证和比较也验证了该方法的合理性和周密性。
[Abstract]:Financial markets are developing with each passing day, and more and more people have been or are participating in them. However, the volatility of financial markets is also obvious to all. For example, stock prices have fluctuated and fluctuated. Therefore, there is always a great risk in investment. VaR(Value at risk is the mainstream method in international financial risk management. It seems that the measurement of VaR is of great practical significance, but whether it can be accurately measured is a statistical problem worth studying and optimizing. VaR is defined as the expected future maximum loss of a financial asset or portfolio over a certain period of time at a normal market level and given confidence level. Normal market level and a certain period of time the financial assets or portfolio will occur or exceed the loss of VaR value at a given probability level. From the definition we can see that the VaR method is closely related to probability and statistics. It can be calculated as a number to represent the maximum loss of financial assets or portfolios for a certain period of time. VaR has its own advantages and disadvantages, but it is difficult to make the results very accurate. We have to consider the problem as thoroughly as possible through constant study to reduce the error. In this paper, we consider the characteristics of peak, thick tail and heteroscedasticity of financial time series data. It is planned to establish ARMA-GARCH (Generalized conditional heteroscedasticity) model based on mixed normal distribution for financial data with these characteristics. Firstly, the characteristics and forms of ARMA-GARCH model, the identification of model and parameter estimation are introduced. This model is the best model to solve the problem of financial data with ARCH effect. Secondly, in view of the peak and thick tail characteristics of financial data, this paper assumes that the random sequence of GARCH model is in mixed normal distribution. Although the GARCH model based on normal distribution can also solve the heteroscedasticity characteristics of volatility, it is insufficient in fitting the thick tail and bias of the data. But the mixed normal distribution not only retains the excellent characteristics of the normal distribution but also solves the defect that the peak and thick tail characteristics can improve the normal distribution to underestimate the value of risk to a certain extent. Thirdly, According to the definition of VaR model, the risk value of the object of study (financial asset or portfolio) is obtained by using the function relationship between the risk value of random sequence based on mixed normal distribution and the risk value of financial asset return in GARCH model. An appropriate set of stock data (Shenzhen Composite Index) is selected for empirical analysis and conclusions are drawn to prove the superiority of this method. Although the new method designed in this paper is more complex in combination structure, However, the model error caused by some problems in previous models is reduced as much as possible, and the rationality and thoroughness of the method are also verified by demonstration and comparison.
【学位授予单位】：西北农林科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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