本文選題：APD分布 + 偏t分布　； 參考：《西南財(cái)經(jīng)大學(xué)》2013年碩士論文

【摘要】：將方差作為風(fēng)險(xiǎn)度量受到很多批評,首先方差無法刻畫風(fēng)險(xiǎn)的非對稱性,其次對于特定分布(如信用風(fēng)險(xiǎn))其二階矩可能不存在。自1994年,J.P.Morgen首次將基于VaR模型的RiskMetric公開,VaR已經(jīng)成為金融業(yè)進(jìn)行風(fēng)險(xiǎn)度量的行業(yè)標(biāo)準(zhǔn)。假定X為代表損益的隨機(jī)變量,F為X的邊際分布函數(shù),VaR的數(shù)學(xué)定義可以如下：VaRα(x)=inf(x∈R,F(x)≥α) VaR在實(shí)踐中獲得了廣泛的應(yīng)用,但其理論存在一些缺陷,眾所周知的一點(diǎn)就是VaR不是一致性風(fēng)險(xiǎn)度量,不滿足次可加性的公理性條件。盡管如此,將VaR定義為一定置信水平下,資產(chǎn)組合在未來特定時(shí)間內(nèi)的最大可能損失,其概念很容易在直覺上被監(jiān)管者、管理層和市場參與者所理解；Danielesson et al.(2005)的研究認(rèn)為盡管存在不少對VaR的批評,但這些問題對于VaR的實(shí)踐不十分重要。目前,已有超過1000家以上的銀行、非金融機(jī)構(gòu)、保險(xiǎn)公司、共同基金和其他資產(chǎn)管理機(jī)構(gòu)宣稱使用VaR來度量金融市場風(fēng)險(xiǎn)。 VaR方法的理論研究,主要集中在以下幾個(gè)方面：一是如何準(zhǔn)確的刻畫損失分布的非對稱和厚尾特征,以提高VaR建模的準(zhǔn)確性；二是如何在眾多計(jì)算方法中選擇合適的方法,因?yàn)榇罅繉?shí)證研究表明不同的VaR估計(jì)方法導(dǎo)致的風(fēng)險(xiǎn)值差異會(huì)很大；三是VaR的評價(jià)體系的建立,到目前為止沒有一個(gè)統(tǒng)一而標(biāo)準(zhǔn)的體系,而如何正確評估模型預(yù)測質(zhì)量是基于VaR方法的金融風(fēng)險(xiǎn)管理的關(guān)鍵；四是非橢圓分布下,VaR不滿足次可加性,不是一個(gè)一致性風(fēng)險(xiǎn)度量,因此如何改進(jìn)VaR模型和尋求替代方法是目前的研究熱點(diǎn)。 為此,本文總結(jié)國內(nèi)外文獻(xiàn)的基礎(chǔ)上,對在VaR的估計(jì)和檢驗(yàn)兩個(gè)方面進(jìn)行相應(yīng)的研究。目前,VaR的估計(jì)存在三種方法,參數(shù)方法(如GARCH方法,RiskMtrics)、半?yún)?shù)方法(如極值理論、CAViaR)和非參數(shù)方法(如歷史模擬法)。非參數(shù)方法與半?yún)?shù)方法的優(yōu)點(diǎn)在于對真實(shí)數(shù)據(jù)的產(chǎn)生過程施加較少的約束和假定,但是這兩種方法在計(jì)算VaR時(shí),很難估計(jì)到VaR的漸進(jìn)協(xié)方差矩陣。參數(shù)估計(jì)方法對損失分布施加了很強(qiáng)的約束,但其易于估計(jì)并容易進(jìn)行后續(xù)檢驗(yàn),但參數(shù)方法估計(jì)的VaR的準(zhǔn)確性很大程度上決定于風(fēng)險(xiǎn)因子損失分布的正確假定。實(shí)證研究表明,金融資產(chǎn)損失分布的尾部并非如同正態(tài)分布那樣呈現(xiàn)指數(shù)平方衰減,更加平緩,尾部較正態(tài)分布更厚。損失分布的另一個(gè)重要特征是非對稱性,即存在杠桿效應(yīng),這是因?yàn)橥顿Y者一般更關(guān)注下方風(fēng)險(xiǎn),即損失邊。Komunjer(2007)認(rèn)為選擇的分布族必須能夠包含最普遍的基準(zhǔn)分布：如正態(tài)分布、拉普拉斯分布,同時(shí)能夠模擬真實(shí)市場數(shù)據(jù)的各種特征：如厚尾和非對稱性,具有閉合的密度函數(shù)形式,以利于估計(jì)和檢驗(yàn)。穩(wěn)定分布(Stable distribution)、Person分布族、Tukey-λ,分布族,能夠擬合很大范圍的偏度和峰度,對金融資產(chǎn)損失分布厚尾和非對稱性的特征具有很好的描述能力,但是這些分布的密度函數(shù)不是封閉形式,因此不能通過最大似然估計(jì)方法來估計(jì)。偏t分布為t分布的擴(kuò)展,亦可用于擬合損失分布的這兩種特征,其在風(fēng)險(xiǎn)度量建模上也有相應(yīng)應(yīng)用,但偏t分布的密度函數(shù)不是對數(shù)凹的,若t分布的自由度小于四,t分布不存在有限的四階距。Gram-Charlier分布的缺點(diǎn)在于必須對偏度和峰度進(jìn)行某些限定,以滿足密度函數(shù)非負(fù)的條件,其最大似然估計(jì)明顯受到初值選擇的影響。因此,本文用Komunjer(2007)提出的非對稱冪分布(APD)來擬合損失分布,以APD-VaR參數(shù)方法為研究對象,以統(tǒng)計(jì)學(xué)和金融學(xué)為研究工具,以定量實(shí)證研究為主,結(jié)合定性分析討論,集中深入地的研究基于APD-VaR方法的金融、風(fēng)險(xiǎn)度量模型的理論與應(yīng)用。探討了APD分布的統(tǒng)計(jì)特性,提出了基于標(biāo)準(zhǔn)GARCH模型的GARCH-APD-VaR參數(shù)方法,闡述了該方法的性質(zhì)、特點(diǎn)和應(yīng)用。 VaR存在多種估計(jì)方法,這意味著對同一資產(chǎn)或資產(chǎn)組合會(huì)導(dǎo)致不同的風(fēng)險(xiǎn)評估,實(shí)證研究表明其差異甚至?xí)浅４�。因�?必須對建立的度量模型進(jìn)行驗(yàn)證,檢驗(yàn)VaR模型預(yù)測質(zhì)量方法有很多,本文討論所謂的“事件概率預(yù)測法”,這種方法是在給定覆蓋率下檢驗(yàn)真實(shí)收益序列對VaR預(yù)測序列的突破過程,包括兩個(gè)部分：非條件覆蓋檢驗(yàn)和獨(dú)立性檢驗(yàn)。目前在應(yīng)用層面上使用較多是似然比檢驗(yàn),該檢驗(yàn)假定數(shù)據(jù)滿足一階馬爾科夫鏈假定,這種約束較強(qiáng)。實(shí)際運(yùn)用中,數(shù)據(jù)可能并不滿足這種的假定,并且該方法未考慮高階自相關(guān)的存在和任何其他外生變量對VaR模型有效性的影響�；诖�,本文引入一種較新的VaR模型驗(yàn)證方法——?jiǎng)討B(tài)分位數(shù)檢驗(yàn)(DQ Test)來作為似然比檢驗(yàn)的補(bǔ)充,建立了似然比檢驗(yàn)和動(dòng)態(tài)分位數(shù)檢驗(yàn)相結(jié)合的VaR評價(jià)體系。 本文的主要研究工作及成果可歸納如下：1.第一章為本文的緒論部分,闡述本文的研究背景,并在系統(tǒng)分析VaR研究現(xiàn)狀的基礎(chǔ)上,指出VaR的研究方向,最后提出了本文要解決的問題,以及研究的意義和創(chuàng)新之處。2.第二章為文獻(xiàn)綜述,筆者對VaR的研究文獻(xiàn)進(jìn)行了梳理,對VaR方法的起源、發(fā)展進(jìn)行了深入的討論；對VaR估計(jì)方法和檢驗(yàn)方法進(jìn)行必要的述評,明了其適用范圍和局限性等。3.第三章為風(fēng)險(xiǎn)管理的理論基礎(chǔ),首先闡述金融風(fēng)險(xiǎn)的概念、特點(diǎn)和分類,詳細(xì)分析了金融市場風(fēng)險(xiǎn)管理的動(dòng)因、功能和管理過程,深入討論了金融市場風(fēng)險(xiǎn)度量方法及其歷史演變,以及金融市場風(fēng)險(xiǎn)的度量框架。4.第四章研究在APD分布假設(shè)下VaR的參數(shù)估計(jì)方法,在這一部分對VaR的原理、定義和計(jì)算方法進(jìn)行了介紹,提出了在偏t分布和APD分布下的動(dòng)態(tài)建模方法。5.第五章主要探討VaR的回溯測試方法,該部分對目前主流的檢驗(yàn)方法的假設(shè)條件、特點(diǎn)和局限性進(jìn)行了必要的分析,在這些分析的基礎(chǔ)上提出了似然比檢驗(yàn)和動(dòng)態(tài)分位數(shù)檢驗(yàn)(DQ檢驗(yàn))相結(jié)合VaR樣本外評價(jià)體系。6.第六章為本文的實(shí)證部分,我們選取上證綜合指數(shù)來進(jìn)行計(jì)量分析,發(fā)現(xiàn)損失分布存在明顯的厚尾和偏斜現(xiàn)象,同時(shí)收益序列存在一階自相關(guān)和二階自相關(guān)現(xiàn)象,這表明引入APD分布和GARCH模型的合理性；從VaR樣本外評估結(jié)果看,如果基于似然比檢驗(yàn),在95%和99%兩個(gè)置信水平下,基于APD分布的VaR都是最優(yōu)模型；動(dòng)態(tài)分位數(shù)檢驗(yàn)下,雖然總體而言APD分布相對其他概率分布函數(shù)有很大優(yōu)勢,但與似然比檢驗(yàn)結(jié)果比較卻有很大的不同,在95%的顯著性水平下僅有少量模型合格,而在99%的置信水平下任何預(yù)測間隔都沒有一個(gè)模型是合格的,由于我們無法觀測到真實(shí)的VaR值,因此這一結(jié)果讓我們關(guān)注到選擇統(tǒng)計(jì)檢驗(yàn)?zāi)Ｐ偷闹匾浴?.第七章為本文的結(jié)論部分,對本文的研究進(jìn)行了總結(jié),并對今后的研究做出了展望。 本文的特色和創(chuàng)新之處在于：提出基于APD分布的動(dòng)態(tài)VaR分析框架,應(yīng)用于基于損益的APD-VaR參數(shù)模型表明APD分布能夠有效的提高VaR的預(yù)測質(zhì)量；提出了似然比檢驗(yàn)和動(dòng)態(tài)分位數(shù)檢驗(yàn)相結(jié)合的風(fēng)險(xiǎn)度量回溯檢驗(yàn)體系。筆者力圖在VaR建模及VaR檢驗(yàn)兩個(gè)方面對VaR理論與應(yīng)用的完善提供一些供有價(jià)值的信息。
[Abstract]:In 1994 , J . P . Morgen first published RiskMetric based on VaR model , VaR has become the industry standard of risk measure in finance industry .

VaR is widely used in practice , but its theory has some drawbacks . It is well known that VaR is not a consistent risk measure . It does not meet the public reason condition of subadditivity . However , VaR is defined as a certain confidence level , and the maximum possible loss of portfolio in future specific time is easily understood by regulators , management and market participants ;
But these problems are not critical to the practice of VaR , though there are not quite a few criticisms of VaR . More than 1,000 banks , non - financial institutions , insurance companies , mutual funds and other asset management agencies have announced the use of VaR to measure financial market risks .

The theoretical research of VaR method focuses on the following aspects : First , how to accurately depict the asymmetric and thick tail features of the loss distribution to improve the accuracy of VaR modeling ;
Second , how to select the right method in many calculation methods , because a large number of empirical studies show that different VaR estimation methods result in a great difference in risk value ;
The third is the establishment of VaR evaluation system , so far there is no unified and standard system , and how to correctly evaluate the model forecast quality is the key to the financial risk management based on VaR method ;
In non - elliptic distribution , VaR does not meet the subadditivity , is not a consistency risk measure , so how to improve VaR model and seek alternative method is the current research hotspot .

In this paper , based on the domestic and foreign literatures , this paper makes a corresponding research on the estimation and test of VaR . At present , there are three methods for estimating VaR . The method of non - parametric method and semi - parametric approach is very difficult to estimate . In this paper , the theory and application of the financial and risk measure model based on APD - VaR method are discussed and discussed in detail . The statistical characteristics of APD distribution are discussed , and the parameter method based on the standard ARCH model is put forward . The property , characteristics and application of the method are expounded .

There are a number of estimation methods for VaR , which means that the same asset or portfolio can lead to different risk assessments . The empirical research shows that the difference is even very large . Therefore , it is necessary to validate the established metric model . This method is based on the assumption that the real revenue sequence is not satisfied with this assumption . In practice , the data may not satisfy this assumption , and the method does not take into account the existence of high - order autocorrelation and any other exogenous variable to the validity of VaR model .

The main research work and achievements of this paper can be summarized as follows : 1 . Chapter 1 is the introduction part of this paper , expounds the research background of this paper , and points out the research direction of VaR based on systematic analysis of the present situation of VaR research , and finally puts forward the problems to be solved in this paper , and the significance and innovation of the research .
In chapter 3 , we introduce the concept , characteristics and classification of risk management in financial markets , and analyze the risk measurement methods and historical evolution of financial markets , and the measurement framework of financial market risk .
Based on the likelihood ratio test , at 95 % and 99 % confidence level , VaR based on APD distribution is the best model .
In the dynamic quantile test , although the APD distribution has a great advantage over other probability distribution functions , it is quite different from the likelihood ratio test results . At the level of 95 % confidence level , only a small number of models are qualified , whereas at 99 % confidence level , there is no model which is acceptable . Therefore , we can not observe the true VaR value .

The characteristics and innovations of this paper are : the dynamic VaR analysis framework based on APD distribution is put forward , and the APD - VaR parameter model based on profit and loss is applied to show that APD distribution can effectively improve the forecasting quality of VaR ;
In this paper , we put forward the risk measurement retrospective test system combining likelihood ratio test and dynamic quantile test . The author tries to provide some valuable information to the improvement of VaR theory and application in VaR modeling and VaR test .

【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.9;F224

【共引文獻(xiàn)】

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本文編號：1779200