本文選題：極值理論　切入點(diǎn)：POT模型　出處：《吉林大學(xué)》2014年碩士論文

【摘要】：近年來,頻繁的金融危機(jī)事件以及金融市場的波動(dòng),使得金融監(jiān)管機(jī)構(gòu)和投資者對(duì)金融資產(chǎn)價(jià)值大幅下滑的波動(dòng)尤為敏感.尖峰、厚尾現(xiàn)象的金融資產(chǎn)收益率序列,也使得傳統(tǒng)的正態(tài)分布假設(shè)受到嚴(yán)重質(zhì)疑.極值理論是解決這類問題較實(shí)用的方法.極值理論包括BMM模型和POT模型,是研究隨機(jī)過程的極值分布及其特征的模型技術(shù).極值理論具有超越樣本數(shù)據(jù)的能力,并能準(zhǔn)確描述分布的尾部. 本文第一章對(duì)極值理論產(chǎn)生的背景進(jìn)行介紹.第二章簡單介紹了BMM模型的原理,包括廣義極值函數(shù)的定義和Fisher Tippett定理,然后詳細(xì)介紹了POT模型的構(gòu)造,廣義帕累托函數(shù)參數(shù)估計(jì)以及風(fēng)險(xiǎn)測量指標(biāo)VaR和ES估計(jì).第三章主要介紹了POT模型中閾值選取的若干方法,例如Hill圖法,指數(shù)回歸模型法和核擬合優(yōu)度統(tǒng)計(jì)量法.第四章介紹了平均超額函數(shù)法，，并在其基礎(chǔ)上提出擬合殘差法，以提高閾值選取的穩(wěn)定性.最后,我們使用上海證券交易所股票價(jià)格綜合指數(shù)2006年1月1日至2007年1月1日的數(shù)據(jù)以及1968-2009年黃金每月價(jià)格來檢驗(yàn)本文所述的POT模型中閾值選取方法的可行性.
[Abstract]:In recent years, frequent financial crises and financial market volatility, which is particularly sensitive to financial regulators and investors to the sharp decline in the value of financial assets. The fluctuation of financial assets return rate series of spikes, thick tail phenomenon, but also makes the traditional assumption of normal distribution has been seriously questioned. Extreme value theory is a method to solve this kind of problem more practical. The extreme value theory including BMM model and POT model, is a model of extreme value distribution and its characteristics of the technology of stochastic process. The extreme value theory has the ability to transcend the sample data, and can accurately describe the tail of the distribution.
This paper introduces the first chapter on the background of extreme value theory. The second chapter simply introduces the principle of BMM model, including the definition of generalized extreme value function and the Fisher Tippett theorem, and then introduces the structure of POT model, generalized Pareto function parameters estimation and risk measurement indexes of VaR and ES estimation. The third chapter mainly introduces several methods to choose the threshold POT model, such as Hill graph method, exponential regression model and kernel goodness of fit method. The fourth chapter introduces the mean excess function method, and puts forward the fitting residual error method on the basis of it, in order to improve the stability of the selected threshold. Finally, we use the Shanghai stock exchange stock price index from January 1, 2006 to January 1, 2007 the data and the 1968-2009 years of gold to test the feasibility of the monthly price threshold selection method of POT model this paper.

【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F224;F830.9

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 劉瓊芳;張宗益;吳俊;;基于指數(shù)回歸模型的中小企業(yè)板極端風(fēng)險(xiǎn)度量[J];管理工程學(xué)報(bào);2011年02期

本文編號(hào)：1702543