發(fā)布時(shí)間：2018-01-16 04:22

  本文關(guān)鍵詞：基于EM估計(jì)的正態(tài)逆高斯分布下中國(guó)股票收益率分布研究　出處：《南京大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 正態(tài)逆高斯分布 尖峰厚尾 股票收益率 EM算法 風(fēng)險(xiǎn)價(jià)值

【摘要】：傳統(tǒng)意義上,我們習(xí)慣用正態(tài)分布來描述金融資產(chǎn)收益率的分布,很多金融模型都是建立在收益率服從正態(tài)分布的假設(shè)基礎(chǔ)之上。但是越來越多的學(xué)者通過經(jīng)驗(yàn)數(shù)據(jù)發(fā)現(xiàn)金融數(shù)據(jù)并非服從正態(tài)分布,我國(guó)學(xué)者吳世龍?jiān)?999年以深圳股票綜合指數(shù)為樣本,驗(yàn)證了中國(guó)證券市場(chǎng)的投資收益率屬于非正態(tài)分布。這是因?yàn)榻鹑跀?shù)據(jù)往往具有尖峰、厚尾、偏態(tài)等特征,已經(jīng)無法用傳統(tǒng)的正態(tài)分布來進(jìn)行準(zhǔn)確刻畫。而國(guó)外學(xué)者研究發(fā)現(xiàn)國(guó)外金融資產(chǎn)的收益率更符合廣義雙曲線分布,針對(duì)本國(guó)的實(shí)際情況,本文力圖通過歷史數(shù)據(jù)驗(yàn)證我國(guó)的股票市場(chǎng)的收益率符合該廣義雙曲線分布下的一個(gè)子類——正態(tài)逆高斯分布,并通過Monte Carlo模擬法驗(yàn)證中國(guó)的股票收益率確實(shí)符合正態(tài)逆高斯分布,而且進(jìn)一步從VaR角度對(duì)這一擬合進(jìn)行了分析,從而得出這種擬合的合理性。由于正態(tài)逆高斯分布參數(shù)估計(jì)的復(fù)雜性,本文在借鑒國(guó)外學(xué)者觀點(diǎn)的基礎(chǔ)上,采用EM算法對(duì)正態(tài)逆高斯分布進(jìn)行參數(shù)估計(jì),并給出正態(tài)逆高斯分布參數(shù)估計(jì)的詳細(xì)過程和實(shí)現(xiàn)步驟。
[Abstract]:In the traditional sense, we are used to describe the distribution of return on financial assets by normal distribution. Many financial models are based on the hypothesis of normal distribution of yield, but more and more scholars find that financial data is not from normal distribution through empirical data. In 1999, Wu Shilong, a Chinese scholar, took Shenzhen stock composite index as a sample to verify that the return on investment in China's securities market belongs to a non-normal distribution. This is because financial data tend to have sharp peaks and thick tails. Skewness and other characteristics can not be accurately characterized by the traditional normal distribution. Foreign scholars found that the return rate of foreign financial assets is more in line with the generalized hyperbolic distribution in accordance with the actual situation in our country. This paper tries to verify that the return rate of stock market in China accords with a subclass-normal inverse Gao Si distribution under the generalized hyperbolic distribution. And through the Monte Carlo simulation method to verify that the Chinese stock returns really accord with the normal inverse Gao Si distribution, and further from the point of view of VaR, this fitting is analyzed. Because of the complexity of parameter estimation of normal inverse Gao Si distribution, this paper uses EM algorithm to estimate the parameter of normal inverse Gao Si distribution on the basis of reference from foreign scholars. The detailed process and implementation steps of normal inverse Gao Si distribution parameter estimation are also given.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F832.51;F224

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本文編號(hào)：1431535