本文選題：BaR　切入點(diǎn)：ARMA-GARCH模型　出處：《西北農(nóng)林科技大學(xué)》2012年碩士論文

【摘要】：金融市場(chǎng)發(fā)展日新月異，越來(lái)越多的人已經(jīng)或者正在參與其中。然而金融市場(chǎng)的波動(dòng)也是有目共睹的，舉個(gè)例子股票的價(jià)格起起落落、變化莫測(cè)，因此人們?cè)谕顿Y時(shí)往往存在很大的風(fēng)險(xiǎn)性。風(fēng)險(xiǎn)價(jià)值簡(jiǎn)稱VaR(Value at Risk)，VaR方法是目前國(guó)際上金融風(fēng)險(xiǎn)管理的主流方法，通過(guò)對(duì)風(fēng)險(xiǎn)進(jìn)行分析、測(cè)度來(lái)盡可能地規(guī)避風(fēng)險(xiǎn)。這樣看來(lái)VaR的度量有很大的現(xiàn)實(shí)意義，但能否準(zhǔn)確得度量它卻是一個(gè)值得研究和優(yōu)化的統(tǒng)計(jì)問(wèn)題。 VaR的定義是，在正常的市場(chǎng)水平和給定置信水平下，一定持有期間內(nèi)金融資產(chǎn)或投資組合預(yù)期未來(lái)可能的最大損失。換句話說(shuō)，正常的市場(chǎng)水平和一定時(shí)期內(nèi)該金融資產(chǎn)或投資組合在給定的概率水平下才會(huì)發(fā)生或超過(guò)VaR值的損失。由定義看出VaR方法與概率統(tǒng)計(jì)息息相關(guān)，它可以通過(guò)計(jì)算被量化為一個(gè)數(shù)字用來(lái)表示一定概率水平下某段時(shí)期金融資產(chǎn)或投資組合的最大損失。VaR的計(jì)算方法很多各有各的優(yōu)缺點(diǎn)，但都很難使結(jié)果非常準(zhǔn)確，我們只有通過(guò)不斷研究盡可能周全得考慮問(wèn)題減小誤差。 本文考慮到金融時(shí)間序列數(shù)據(jù)經(jīng)常出現(xiàn)的尖峰厚尾和異方差特性，，計(jì)劃針對(duì)存在這些特性的金融數(shù)據(jù)建立基于混合正態(tài)分布的ARMA-GARCH(廣義條件異方差)模型。首先介紹ARMA-GARCH模型的特性與形式、模型的識(shí)別和參數(shù)估計(jì)等，這一模型是解決具有ARCH效應(yīng)的金融數(shù)據(jù)的最佳模型。其次，針對(duì)金融數(shù)據(jù)的尖峰厚尾特性，本文將假定GARCH模型的隨機(jī)序列服從混合正態(tài)分布，因?yàn)殡m然基于正態(tài)分布下GARCH模型也能解決波動(dòng)率的異方差特性，但它在擬合數(shù)據(jù)的厚尾性和有偏性時(shí)顯得不足，而混合正態(tài)分布既保留了正態(tài)分布的優(yōu)良特性又能在一定程度上解決尖峰厚尾特性適當(dāng)?shù)母纳普龖B(tài)分布低估風(fēng)險(xiǎn)價(jià)值的缺陷。再次，根據(jù)VaR模型的定義利用GARCH模型中隨機(jī)序列基于混合正態(tài)分布的風(fēng)險(xiǎn)價(jià)值與金融資產(chǎn)收益率的風(fēng)險(xiǎn)價(jià)值的函數(shù)關(guān)系得到研究對(duì)象（金融資產(chǎn)或投資組合）的風(fēng)險(xiǎn)價(jià)值。最后，選取一組合適的股票數(shù)據(jù)（深證綜指）利用本文研究方法進(jìn)行實(shí)證分析并得出結(jié)論證明該方法的優(yōu)越性。本文設(shè)計(jì)的這種新方法雖然在組合結(jié)構(gòu)上較顯復(fù)雜，但考慮問(wèn)題較周全（盡可能地去減少以往模型中由于一些問(wèn)題引起的模型誤差），經(jīng)過(guò)實(shí)證和比較也驗(yàn)證了該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.
【學(xué)位授予單位】：西北農(nóng)林科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類(lèi)號(hào)】：F224;F830.9

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