【摘要】：隨機(jī)波動率模型自建立以來,在金融時間序列波動率建模中得到了廣泛的應(yīng)用,但是由于SV模型波動率的潛藏性,使得傳統(tǒng)的似然函數(shù)極其復(fù)雜,這導(dǎo)致SV模型在最大似然估計方面面臨著一定的困難.而Bayes方法結(jié)合了參數(shù)的先驗信息和后驗分布,在SV模型的參數(shù)估計方面具有一定的優(yōu)勢,基于MCMC方法的Bayes估計在實際應(yīng)用中具有較好的精確度.因此,本文通過Bayes方法來研究SV模型的參數(shù)估計問題,并且利用MCMC方法進(jìn)行了計算和實證分析.根據(jù)參數(shù)的估計的結(jié)果,得出在刻畫中國銀行和交通銀行的收益率序列時,厚尾SV模型的模擬效果要優(yōu)于標(biāo)準(zhǔn)SV模型.本文主要研究SV模型的參數(shù)估計方法,其中是將標(biāo)準(zhǔn)SV模型和厚尾SV模型進(jìn)行對比研究,主要內(nèi)容如下:1.論文介紹了金融市場的波動率,波動率在金融時間序列中表現(xiàn)出的特征以及相應(yīng)的預(yù)備知識.2.論文對標(biāo)準(zhǔn)SV模型和厚尾SV模型進(jìn)行了詳細(xì)的結(jié)構(gòu)分析,得到SV模型的似然函數(shù)表現(xiàn)形式.3.論文在SV模型的參數(shù)估計中使用的是MCMC方法,該方法結(jié)合了貝葉斯估計方法,在抽樣過程中使用的是Gibbs抽樣方法.在貝葉斯估計法中,推導(dǎo)了后驗分布的理論公式.并且將后驗分布理論公式運(yùn)用到SV模型中,推導(dǎo)出了標(biāo)準(zhǔn)SV模型和厚尾SV模型的每個待估參數(shù)的后驗分布函數(shù).4.論文在實證分析中,使用Win Bugs軟件得到參數(shù)估計的結(jié)果,根據(jù)模型對數(shù)據(jù)的擬合效果,以及模型DIC值的比較,通過得到的結(jié)果對比分析了標(biāo)準(zhǔn)SV模型和厚尾SV模型的模擬效果,得到厚尾SV模型的擬合效果更優(yōu).
[Abstract]:Since the establishment of stochastic volatility model, it has been widely used in financial time series volatility modeling. However, because of the latent volatility of SV model, the traditional likelihood function is extremely complex. This leads to some difficulties in maximum likelihood estimation for SV model. The Bayes method combines the prior information and the posterior distribution of the parameters, so it has some advantages in the parameter estimation of the SV model. The Bayes estimation based on the MCMC method has good accuracy in practical application. Therefore, the Bayes method is used to study the parameter estimation of SV model, and the MCMC method is used to calculate and analyze the model. According to the result of parameter estimation, it is concluded that the simulation effect of the thick tail SV model is better than that of the standard SV model in describing the return sequence of Bank of China and Bank of Communications. In this paper, we mainly study the parameter estimation method of SV model, in which the standard SV model and the thick-tailed SV model are compared. The main contents are as follows: 1. This paper introduces the volatility of financial market, the characteristics of volatility in financial time series and the corresponding preparatory knowledge. In this paper, the standard SV model and the thick-tailed SV model are analyzed in detail, and the expression form of likelihood function of SV model is obtained. In this paper, the MCMC method is used in the parameter estimation of SV model, which combines Bayesian estimation method and Gibbs sampling method in the sampling process. In Bayesian estimation, the theoretical formula of posterior distribution is derived. The posterior distribution function of the standard SV model and the thick-tailed SV model is derived by applying the posterior distribution formula to the SV model. In the empirical analysis, the results of parameter estimation are obtained by using Win Bugs software. According to the fitting effect of the model and the comparison of the DIC value of the model, the simulation results of the standard SV model and the thick-tailed SV model are compared and analyzed. The fitting effect of SV model with thick tail is better.
【學(xué)位授予單位】：中國礦業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.8

【參考文獻(xiàn)】

相關(guān)期刊論文 前7條

1 周孝華;張保帥;;基于SV-GED模型的極值風(fēng)險度量研究[J];管理工程學(xué)報;2014年01期

2 朱慧明;李素芳;虞克明;曾慧芳;林靜;;基于Gibbs抽樣的貝葉斯金融隨機(jī)波動模型分析[J];湖南大學(xué)學(xué)報(自然科學(xué)版);2008年12期

3 劉樂平;張美英;李姣嬌;;基于WinBUGS軟件的貝葉斯計量經(jīng)濟(jì)學(xué)[J];東華理工學(xué)院學(xué)報(社會科學(xué)版);2007年02期

4 李付軍;;SV-GED模型在中國股市的VaR與ES度量及分析[J];系統(tǒng)工程理論方法應(yīng)用;2006年01期

5 余素紅,張世英;SV和GARCH模型擬合優(yōu)度比較的似然比檢驗[J];系統(tǒng)工程學(xué)報;2004年06期

6 余素紅,張世英,宋軍;基于GARCH模型和SV模型的VaR比較[J];管理科學(xué)學(xué)報;2004年05期

7 余素紅,張世英;SV與GARCH模型對金融時間序列刻畫能力的比較研究[J];系統(tǒng)工程;2002年05期

，

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