【作者】 金晓燕；

【导师】 边宽江；

【作者基本信息】 西北农林科技大学 ， 应用数学， 2012， 硕士

【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。更多还原

【Abstract】 The financial market is developing rapidly and more and more people have already beenor are involved in it now. However, the fluctuation in financial market is obvious to people,taking stock as an example, the ups and downs of the price make the stock market changconstantly. So people are always facing with great risk while investing in finance.VaR is theabbreviation of value at risk. VaR method which is based on risk analysis and measurement inorder to avoid risk as much as possible is currently the principle method on financial riskmeasurement. Thus the calculation of VaR actually has great realistic significance, yetweather we can calculate it exactly is still a statistical problem which is worth to study andoptimize further.The definition of VaR is the expected future maximum loss of some financial asset orportfolio within a certain period in normal market conditions and a given confidence level. Inother words, the financial asset or portfolio occurs or exceeds the value at risk only in thegiven probability level. As the definition shows, VaR method is closely related withpossibility statistics and can express the financial asset’s or portfolio’s maximum loss within acertain period in given possibility level using a calculated number. Although there are lots ofmethods to calculate VaR and each one has its own merits and drawbacks, yet it’s still difficultto get a very accurate result, so we can only try our efforts to research constantly and considercomprehensively to reduce the error.Aming at the characteristics of kurtosis and heteroscedasticity that financial timeseries often occurs, we plan to build ARMA-GARCH Model based on mixed normaldistribution in this paper. Firstly, the characteristic and form of ARMA-GARCH Model andits identification and the parameters’ estimation will be introduced, as this model is the optimal one to resolve ARCH effect. Secondly, aming at the characteristics mentioned above,we assume that the random sequence of GARCH model obeys mixed normal distribution.Although GARCH model based on normal distribution can solve heteroscedasticity to somedegree, yet it’s insufficient when fitting the data which has thick tail and partial characteristics.Instead, mixed normal distribution can not only retain the advantages of normal distributionbut also solve the kurtosis characteristic and thus improve the defect that normal distributionunderestimates value at risk. Thirdly, we will get the financial asset’s or portfolio’s value atrisk using the function relations between itself and the VaR of random sequences in GARCHmodel which has been calculated by the definition. At last, a suitable group of stockdata(Shenzhen composite index) will be selected for empirical analysis to get a conclusionwhich proves the superiority of the method we study in this paper. Maybe the compositestructure of this newly designed method seems a little complex, yet it’s very comprehensive totry efforts to reduce the errors which are usually caused in the previous models, and after theempirical analysis and comparison with others this method is proved to be reasonable andaccurate.更多还原