本文選題：EGARCH模型　切入點：擬隨機(jī)數(shù)　出處：《上海大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：波動性(Volatility)是證券市場的一個重要特性，是數(shù)量經(jīng)濟(jì)學(xué)和統(tǒng)計科學(xué)面臨的最重要問題之一，與金融市場的功能、穩(wěn)定性密切相關(guān)，在金融資產(chǎn)定價和資產(chǎn)配中處于十分總要的位置，是體現(xiàn)資本市場價格行為、質(zhì)量和效率的有效指標(biāo)之一。對于一個發(fā)展比較成熟的資本市場而言，應(yīng)該有比較適度的微小波動，而頻繁和波幅過大的震蕩不僅對投資者做出正確的投資組合策略不利，也會危害整個金融市場的健康、穩(wěn)定和發(fā)展，甚至可能誘發(fā)全球性金融危機(jī)，所以證券市場的收益率波動特征以及影響因素備受各研究學(xué)者的關(guān)注。2010年我國推出滬深了300股指期貨，股票市場波動問題變得更加復(fù)雜。本文就是在這樣的背景下開始對我國滬深300股票指數(shù)的研究，在研究方法上由于股票指數(shù)序列存在自相關(guān)與異方差的問題，不能再應(yīng)用傳統(tǒng)意義上的收益率和風(fēng)險度量方法，因此需要基于ADF的單位根檢驗(Unit Root Test)、協(xié)整檢驗，最終通過建立EGARCH模型來反映股票市場帶有非對稱性的波動特性。 本文系統(tǒng)闡述了ARCH類模型的基本理論，分析了ARCH類模型的基本性質(zhì)特征，并著重探討了這類模型的參數(shù)估計方法。極大似然估計方法是現(xiàn)階段最廣泛使用的參數(shù)估計方法。雖然有學(xué)者提出了BHHH算法和廣義矩方法等一些較為先進(jìn)的算法來得到模型參數(shù)的分布，并以此獲取模型參數(shù)更多的信息。然而在實際運算中這類算法常遇到中間數(shù)據(jù)震蕩從而導(dǎo)致算法整體失效的問題。也有學(xué)者選擇了使用馬爾科夫鏈Monte Carlo(MCMC)方法來計算ARCH類模型的后驗分布，然而該方法需要采取如Griddy-Gibbs，Metropolis-Hastings等較為復(fù)雜的抽樣方法，使用起來很不方便。國內(nèi)有學(xué)者提出了一種估計GARCH(1,1)模型參數(shù)的簡便有效的常規(guī)Monte Carlo方法，本文在該工作基礎(chǔ)上，選擇Halton序列替代原方法中的均勻分布作為參數(shù)的先驗分布，并將該方法從GARCH（1,1）模型推廣到EGARCH模型。最終表明了這種方法在估計EGARCH模型參數(shù)時的有效性。 本文主要從以下幾個方面進(jìn)行研究： 1)系統(tǒng)地闡述了自回歸條件異方差回歸模型族的產(chǎn)生背景，統(tǒng)計意義，以及當(dāng)前國內(nèi)外的研究現(xiàn)狀與發(fā)展水平等。并詳細(xì)介紹了本文使用的常規(guī)MonteCarlo方法的理論基礎(chǔ)——Bayes推斷理論。 2)詳細(xì)闡述了擬蒙特卡洛方法的理論部分，并通過MATLAB軟件設(shè)計實驗，對比分析了擬隨機(jī)數(shù)與偽隨機(jī)數(shù)的區(qū)別，通過實驗結(jié)果來直觀地呈現(xiàn)本文使用擬隨機(jī)數(shù)代替?zhèn)坞S機(jī)數(shù)的原因——擬隨機(jī)數(shù)用有的更好的統(tǒng)計特性。 3)結(jié)合我國的股票市場，在實證分析中通過對滬深300指數(shù)時間序列數(shù)據(jù)的分析，建立EGARCH模型，，并給出了該模型參數(shù)的具體的常規(guī)擬蒙特卡洛估計方法，通過與最大似然估計方法對比，證明了該方法的有效性。
[Abstract]:Volatility volatility is an important characteristic of securities market. It is one of the most important problems faced by quantitative economics and statistical science. It is closely related to the function and stability of financial market. It is one of the most effective indicators of capital market price behavior, quality and efficiency in financial asset pricing and asset allocation. There should be moderate small fluctuations, and frequent and excessive volatility is not only bad for investors to make the right portfolio strategy, but also endangers the health, stability and development of the entire financial market. It may even lead to a global financial crisis, so the volatility characteristics of the yield and the influencing factors of the securities market have attracted the attention of various researchers. In 2010, China launched the Shanghai and Shenzhen 300 stock index futures. The volatility of stock market has become more complicated. This paper begins to study the stock index of Shanghai and Shenzhen 300 stock index in China under this background. In the research method, because of the problem of autocorrelation and heteroscedasticity in stock index sequence, The traditional methods of yield and risk measurement can no longer be applied, so the unit root test based on ADF and the cointegration test are needed. Finally, the EGARCH model is established to reflect the asymmetric volatility of the stock market. In this paper, the basic theory of ARCH class model is expounded, and the basic properties of ARCH class model are analyzed. The maximum likelihood estimation method is the most widely used parameter estimation method at present. Although some scholars have put forward some advanced algorithms such as BHHH algorithm and generalized moment method, etc. To get the distribution of model parameters, And get more information about the model parameters. However, in the actual operation, this kind of algorithms often encounter the problem of intermediate data oscillation, which leads to the overall failure of the algorithm. Some scholars have also chosen to use the Markov chain Monte method to calculate the problem. The posterior distribution of ARCH model is calculated. However, this method needs more complicated sampling methods such as Griddy-Gibbsl Metropolis-Hastings, which is very inconvenient to use. Some domestic scholars have proposed a simple and effective conventional Monte Carlo method to estimate the parameters of the GARCH1) model. The Halton sequence is used to replace the uniform distribution in the original method as the prior distribution of the parameters, and the method is extended from the Garch 1 / 1) model to the EGARCH model. Finally, the effectiveness of this method in estimating the parameters of the EGARCH model is demonstrated. This article mainly carries on the research from the following several aspects:. 1) the background of autoregressive conditional heteroscedasticity regression model family, its statistical significance, the current research status and development level at home and abroad, etc., and the theoretical basis of the conventional MonteCarlo method used in this paper, the Bayesian inference theory, are introduced in detail. 2) the theoretical part of quasi Monte Carlo method is expounded in detail, and the difference between pseudo random number and pseudorandom number is compared and analyzed by MATLAB software design experiment. The experimental results show the reason why pseudorandom numbers are replaced by pseudorandom numbers in this paper, which has better statistical characteristics. 3) combining the stock market of our country, through the analysis of the time series data of CSI 300 index, the EGARCH model is established, and the concrete method of quasi Monte Carlo estimation of the parameters of this model is given. The effectiveness of the proposed method is proved by comparison with the maximum likelihood estimation method.
【學(xué)位授予單位】：上海大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F832.51;F224

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