本文關(guān)鍵詞： VaR ES 廣義極值分布 廣義Pareto分布 Poisson-GP復(fù)合超閾值分布　出處：《重慶大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：在金融風險管理領(lǐng)域中，學(xué)者們已經(jīng)得到許多基于正態(tài)分布假設(shè)的研究方法以及資產(chǎn)配置技術(shù)和套利策略等。極端的金融風險鮮有發(fā)生，但一旦出現(xiàn)極值事件，就會給人類的生產(chǎn)和生活帶來難以承擔的惡劣影響。特別是1970年以后，金融市場出現(xiàn)了極大波動，金融資產(chǎn)暴漲、暴跌變得尤為常見。傳統(tǒng)的基于高斯正態(tài)分布假定的理論研究受到廣大學(xué)者的嚴重質(zhì)疑。對金融資產(chǎn)收益率序列尾部特征的研究正是基于此產(chǎn)生的，它是近幾十年來發(fā)展起來的，是金融市場極端風險度量的重要內(nèi)容之一。怎樣使金融資產(chǎn)收益率序列的尾部特征得以有效描述，得到其近似分布函數(shù)，進而準確得到各類風險度量模型的參數(shù)估計和其置信區(qū)間，在理論研究和實際應(yīng)用中都具有非常重要的意義和價值。本論文圍繞基于極值理論和復(fù)合極值模型的風險度量方法展開深入的學(xué)習(xí)和研究。主要研究內(nèi)容如下： 系統(tǒng)地闡述和分析了BMM模型和POT模型的思想、原理和方法，并對這兩種極值模型的優(yōu)缺點進行了比較；針對被廣泛應(yīng)用的廣義極值分布，本文介紹了其概念以及具體的三種類型，分別討論了他們的最大值吸引場；給出了廣義Pareto分布的原理，分析了其參數(shù)估計和計算金融資產(chǎn)收益率的VaR和ES值的方法，研究了POT模型中閾值的選取標準，，詳細介紹了確定閾值的三種方法；對Poisson-Gumbel復(fù)合極值模型作簡單介紹，在此基礎(chǔ)上，結(jié)合Poisson分布與廣義Pareto分布，賦予變量新的意義，得到新的分布——Poisson-GP復(fù)合超閾值分布，討論并比較了該分布的三種參數(shù)估計方法——極大似然法、概率權(quán)矩法以及復(fù)合矩法，其估計效果顯示，極大似然法最佳；最后采用廣義Pareto分布和Poisson-GP復(fù)合超閾值分布，對上證指數(shù)1996-2013年間的日收益率序列進行了實證分析，利用POT模型來計算風險價值VaR和ES，對相應(yīng)參數(shù)進行了估計，最終獲得該金融數(shù)據(jù)的極端風險度量，結(jié)果顯示了兩個模型對金融資產(chǎn)收益率的擬合效果好、精度較高、能反映數(shù)據(jù)厚尾特征的優(yōu)良性質(zhì)；最后，總結(jié)本論文的不足之處并提出進一步的研究方向。
[Abstract]:In the field of financial risk management, scholars have obtained many research methods based on normal distribution hypothesis, asset allocation technology and arbitrage strategy, etc. Extreme financial risks rarely occur, but once extreme events occur, It will have an unbearable adverse impact on human production and life. Especially after 1970, financial markets have experienced great fluctuations and financial assets have soared. The traditional theoretical research based on Gao Si's normal distribution hypothesis has been seriously questioned by many scholars. It has been developed in recent decades and is one of the important contents of extreme risk measurement in financial market. How to describe the tail feature of financial asset return series effectively and obtain its approximate distribution function, Then the parameter estimation and confidence interval of various risk measurement models are obtained accurately. This paper focuses on the risk measurement method based on extreme value theory and compound extreme model. The main research contents are as follows:. The ideas, principles and methods of BMM model and POT model are systematically expounded and analyzed, and the advantages and disadvantages of these two extreme value models are compared. In this paper, the concept and three specific types are introduced, their maximum attraction fields are discussed, the principle of generalized Pareto distribution is given, and the methods of estimating its parameters and calculating the VaR and es values of financial asset returns are analyzed. In this paper, the criteria of threshold selection in POT model are studied, three methods of determining threshold are introduced in detail, and the Poisson-Gumbel compound extreme value model is simply introduced. On this basis, combining the Poisson distribution with the generalized Pareto distribution, the variables are given new significance. A new distribution Poisson-GP composite over-threshold distribution is obtained. Three parameter estimation methods, maximum likelihood method, probabilistic weight moment method and compound moment method, are discussed and compared. The results show that the maximum likelihood method is the best. Finally, by using generalized Pareto distribution and Poisson-GP composite over-threshold distribution, the daily yield series of Shanghai stock index from 1996 to 2013 are empirically analyzed. The POT model is used to calculate the risk value VaR and ESS, and the corresponding parameters are estimated. Finally, the extreme risk measurement of the financial data is obtained. The results show that the two models have good fitting effect on the return rate of financial assets, and the accuracy is high, which can reflect the excellent properties of the data with thick tail. Summarize the deficiency of this paper and put forward the further research direction.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F830.9;O211.3

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