【摘要】：股指收益率分布一直是金融研究中的一個(gè)重要問(wèn)題。研究股指收益率分布,不僅有助于認(rèn)識(shí)股票市場(chǎng)的內(nèi)在運(yùn)行規(guī)律,而且還可以幫助股指期貨投資者進(jìn)行正確的風(fēng)險(xiǎn)度量,以便進(jìn)行資產(chǎn)定價(jià)與資產(chǎn)組合選擇。提出能夠更好地?cái)M合金融資產(chǎn)收益率的分布,并對(duì)其進(jìn)行統(tǒng)計(jì)分析已成為金融研究的新的重要課題之一。本文首先對(duì)非對(duì)稱(chēng)兩參數(shù)Laplace分布的統(tǒng)計(jì)分析進(jìn)行了研究。運(yùn)用矩估計(jì),極大似然等方法進(jìn)行了參數(shù)估計(jì),證明了極大似然估計(jì)法與矩估計(jì)2的結(jié)果實(shí)際是一致的。并用Monte-Carlo模擬綜合比較了幾種估計(jì)方法,得出矩估計(jì)2比矩估計(jì)1精度更好的結(jié)論。其次,本文研究了非對(duì)稱(chēng)三參數(shù)Laplace分布的統(tǒng)計(jì)分析及參數(shù)估計(jì)。從現(xiàn)有文獻(xiàn)來(lái)看,關(guān)于非對(duì)稱(chēng)三參數(shù)Laplace分布的參數(shù)估計(jì)都是通過(guò)極大似然的方法獲得,但其極大似然估計(jì)的存在性和唯一性理論證明并不完善。本文給出一種較為簡(jiǎn)單的處理方法。并用模擬綜合比較了幾種參數(shù)估計(jì)方法。接著,本文指出了周靜怡[23]一文中參數(shù)估計(jì)值的錯(cuò)誤并給出了修正后的參數(shù)估計(jì)值,進(jìn)行了擬合優(yōu)度檢驗(yàn)。同時(shí)運(yùn)用上文中提出的參數(shù)估計(jì)方法,對(duì)文章中的數(shù)據(jù)進(jìn)行了參數(shù)估計(jì),擬合優(yōu)度檢驗(yàn)后的結(jié)果表明非對(duì)稱(chēng)三參數(shù)Laplace分布能夠較好的描述樣本數(shù)據(jù)尖峰,厚尾,偏態(tài)的特征。最后,本文對(duì)滬,深兩市股指日,周收益率進(jìn)行了實(shí)證研究。研究結(jié)果表明,非對(duì)稱(chēng)三參數(shù)Laplace分布比正態(tài)分布能夠更好的擬合滬,深兩市股指日,周收益率。
[Abstract]:The distribution of stock index yield is always an important problem in financial research. The study of the distribution of stock index yield is not only helpful to understand the inherent law of stock market, but also helps investors to measure the risk correctly, so as to make asset pricing and portfolio selection. It is proposed that the distribution of the return rate of financial assets can be fitted better and the statistical analysis of it has become one of the new and important subjects in financial research. In this paper, the statistical analysis of asymmetric two-parameter Laplace distribution is studied. The method of moment estimation, maximum likelihood and so on is used to estimate the parameters, and it is proved that the results of maximum likelihood estimation and moment estimation are in good agreement with each other. Several estimation methods are synthetically compared with Monte-Carlo simulation. It is concluded that the moment estimation 2 is more accurate than the moment estimation 1. Secondly, this paper studies the statistical analysis and parameter estimation of asymmetric three parameter Laplace distribution. According to the existing literatures, the parameter estimation of asymmetric three-parameter Laplace distribution is obtained by the method of maximum likelihood, but the existence and uniqueness theory of maximum likelihood estimation is not perfect. In this paper, a relatively simple treatment method is given. Several parameter estimation methods are compared by simulation. Then, this paper points out the error of parameter estimation in Zhou Jingyi [23], gives the revised parameter estimate, and tests the goodness of fit. At the same time, the parameter estimation method mentioned above is used to estimate the parameters of the data in this paper. The results of goodness of fit test show that the asymmetric three-parameter Laplace distribution can well describe the peak, thick tail and skewness characteristics of the sample data. Finally, this paper makes an empirical study on the daily and weekly returns of stock indexes in Shanghai and Shenzhen stock markets. The results show that the asymmetric three-parameter Laplace distribution can better fit the daily and weekly returns of Shanghai and Shenzhen stock indexes than the normal distribution.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O212.1

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