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

  更多相關文章： 正態(tài)逆高斯分布 尖峰厚尾 股票收益率 EM算法 風險價值

【摘要】：傳統(tǒng)意義上,我們習慣用正態(tài)分布來描述金融資產收益率的分布,很多金融模型都是建立在收益率服從正態(tài)分布的假設基礎之上。但是越來越多的學者通過經驗數據發(fā)現(xiàn)金融數據并非服從正態(tài)分布,我國學者吳世龍在1999年以深圳股票綜合指數為樣本,驗證了中國證券市場的投資收益率屬于非正態(tài)分布。這是因為金融數據往往具有尖峰、厚尾、偏態(tài)等特征,已經無法用傳統(tǒng)的正態(tài)分布來進行準確刻畫。而國外學者研究發(fā)現(xiàn)國外金融資產的收益率更符合廣義雙曲線分布,針對本國的實際情況,本文力圖通過歷史數據驗證我國的股票市場的收益率符合該廣義雙曲線分布下的一個子類——正態(tài)逆高斯分布,并通過Monte Carlo模擬法驗證中國的股票收益率確實符合正態(tài)逆高斯分布,而且進一步從VaR角度對這一擬合進行了分析,從而得出這種擬合的合理性。由于正態(tài)逆高斯分布參數估計的復雜性,本文在借鑒國外學者觀點的基礎上,采用EM算法對正態(tài)逆高斯分布進行參數估計,并給出正態(tài)逆高斯分布參數估計的詳細過程和實現(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.
【學位授予單位】：南京大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F832.51;F224

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本文編號：1431535