本文選題：非對稱拉普拉斯分布　切入點：非對稱指數(shù)冪分布　出處：《南京財經(jīng)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：貝葉斯分位數(shù)回歸方法是近年來國內(nèi)外的研究熱點,把貝葉斯分位數(shù)回歸方法應(yīng)用于金融風(fēng)險測度是一個重要的研究課題,而計算風(fēng)險價值VaR是金融市場風(fēng)險測度的主流方法.本文探討基于貝葉斯分位數(shù)自回歸方法的VaR建模,并用該方法研究香港恒生指數(shù)的VaR風(fēng)險測度.第一章闡述了選題的背景以及研究意義,并進行了國內(nèi)外文獻綜述.第二章是基本概念及其方法的簡要概述,包括：分位數(shù)回歸,貝葉斯分析的相關(guān)理論和方法,以及VaR的概念與主要性質(zhì).第三章從理論上構(gòu)建了基于貝葉斯分位數(shù)自回歸的VaR建模框架.本章分成兩大部分.第一部分,分別針對誤差項服從非對稱拉普拉斯分布(ALD)和誤差項服從非對稱指數(shù)冪分布(AEPD)的分位數(shù)回歸模型,通過設(shè)定參數(shù)的先驗分布及確定樣本的似然函數(shù),根據(jù)貝葉斯原理,利用MCMC中算法按照參數(shù)的滿條件后驗分布交替采樣,得到具有平穩(wěn)分布的馬氏鏈的一個樣本實現(xiàn),該平穩(wěn)分布就是參數(shù)的后驗分布.由于均方誤差損失下,參數(shù)的最優(yōu)貝葉斯估計就是其后驗均值,所以可以用馬氏鏈的樣本均值作為參數(shù)的最優(yōu)估計.值得說明的是：由于ALD和AEPD都是非標(biāo)準分布,所以在采樣前,本文對它們的似然函數(shù)進行了變換.第二部分,作為上述貝葉斯分位數(shù)回歸模型的一種特殊類型,遵循上述思路,構(gòu)建了貝葉斯分位數(shù)自回歸VaR模型,具體做法是：在提出了分位數(shù)自回歸VaR模型之后,按照AIC信息選擇準則給出此模型的定階方法,利用第一部分給出的方法對參數(shù)進行貝葉斯估計,并給出不同分位水平下VaR模型的評價方法.第四章是在第三章給出的理論建�？蚣艿幕A(chǔ)上,將貝葉斯分位數(shù)自回歸VaR模型應(yīng)用于香港恒生指數(shù)的風(fēng)險測度中.選取香港恒生指數(shù)2010年1月4日到2014年1月10日收盤價,通過對數(shù)變換后獲得對數(shù)收益率數(shù)據(jù),再從均值、標(biāo)準差、偏度、峰度、JB統(tǒng)計量、ADF值、自相關(guān)系數(shù)與偏相關(guān)系數(shù)幾個方面,對這些數(shù)據(jù)進行特征分析后,發(fā)現(xiàn)了數(shù)據(jù)具有非正態(tài)性、尖峰厚尾性、平穩(wěn)性和自相關(guān)性,因而能確定本章模型類型隸屬于第三章的貝葉斯分位數(shù)自回歸VaR模型.根據(jù)第三章構(gòu)建的理論建�？蚣�,首先應(yīng)用AIC信息準則確定模型的自回歸階數(shù)為5階.然后,選取卡方分布為σ的先驗分布,其余參數(shù)則選取正態(tài)分布為先驗分布,按照3.1節(jié)和3.2節(jié)給出的似然函數(shù),根據(jù)貝葉斯原理,利用第三章給出的MCMC算法結(jié)合R語言中的R2WinBUGS,得到了香港恒生指數(shù)分位水平分別為0.01、0.025與0.05的貝葉斯分位數(shù)自回歸VaR模型的參數(shù)估計、各個參數(shù)的后驗密度圖、動態(tài)迭代圖以及GR統(tǒng)計量收斂性圖.通過對上述結(jié)果的一系列分析表明：基于ALD的貝葉斯分位數(shù)自回歸VaR模型和基于AEPD的貝葉斯分位數(shù)自回歸VaR模型的各個分位水平下的馬氏鏈均是收斂的,且參數(shù)估計的誤差較小.此外分別從同一分位水平角度比較了不同滯后期的自變量對VaR值的影響,以及從不同分位水平下同一滯后期的自變量對VaR值的影響.根據(jù)上述所建的模型可以計算不同置信水平(分別對應(yīng)不同的分位水平)下的香港恒生指數(shù)的VaR值.通過比較VaR實際值和VaR估計值,可知大部分VaR實際值小于VaR估計值,說明大部分損失在模型預(yù)測之內(nèi).同時通過比不同置信水平的VaR實際值和VaR估計值可知,置信水平越高,估計越保守,實際值超過預(yù)測值的可能性越小.第五章應(yīng)用Kupiec失敗率檢驗法,對第四章所建的基于ALD的貝葉斯分位數(shù)自回歸VaR模型和基于AEPD的貝葉斯分位數(shù)自回歸VaR模型進行效果評價.通過得到的失敗區(qū)間、失敗數(shù)、失敗率、LR值以及LR臨界值來比較兩個模型,結(jié)果表明：基于AEPD的VaR模型比基于ALD的VaR模型的失敗數(shù)更少,失敗率更小.并把基于AEPD的VaR模型與計算VaR的傳統(tǒng)的歷史模擬法進行比較.結(jié)果發(fā)現(xiàn)基于AEPD的VaR模型效果更好.最后在第六章,對全文進行了總結(jié)與展望.
[Abstract]:Bias quantile regression method is a research hotspot in recent years, the Bias quantile is an important research topic of regression method is applied to the measure of financial risk, and calculate the risk value of VaR is the mainstream method of financial market risk measurement. This paper discusses Bayesian quantile regression method based on the VaR model, and use the VaR risk measure method research of Hongkong's Hang Seng Index. The first chapter introduces the background and significance of the research, and conducted a literature review at home and abroad. The second chapter is a brief overview of the basic concepts and methods, including: Quantile Regression, correlation theory and method of Bias analysis, as well as the VaR concept and the main properties of third. The chapter constructs a theoretical framework of VaR modeling based on quantile regression of Bias. This chapter is divided into two parts. The first part, according to the error terms are subject to asymmetric pull. The Gaussian distribution (ALD) and the error term to asymmetric exponential power distribution (AEPD) of the quantile regression model, the prior distribution and determine the likelihood function of sample set parameters, according to the Bias principle, using the MCMC algorithm in accordance with the full conditional posterior distributions of parameters of alternating sampling, a Markov chain with stationary distribution of samples the realization of the stationary distribution is the posterior distribution of the parameters. The mean square error loss, Bias optimal estimation of the parameters is the posterior mean, so the optimal Markov chain can be used as a parameter of the sample mean estimate. It is worth noting: because ALD and AEPD are non standard distribution, so the sampling in this paper, the likelihood function on the transformation. The second part, a special type of Bias as the quantile regression model, according to the above thinking, Bias constructed the quantile regression VaR Model, the specific approach is: in the proposed quantile regression VaR model, according to the selection criteria of this model are given AIC information to determine the order of the Bias method for parameter estimation method using the first part gives the evaluation method of VaR model and give different levels. The fourth chapter is based on theoretical modeling framework third the chapter on the Bias risk measure digit autoregressive VaR model is applied to Hongkong's Hang Seng Index. From Hongkong's Hang Seng Index from January 4, 2010 to January 10, 2014 closing price, by the logarithmic transformation obtained after logarithm yield data from the mean, standard deviation, skewness, kurtosis, JB statistics, ADF value, correlation coefficient and the partial correlation coefficients of several aspects, analyze the characteristics of the data, that data is non normal, fat tail, stationarity and autocorrelation, which can determine this chapter Bias type model belongs to the third chapter of the quantile regression VaR model. According to the third chapter constructs the theoretical framework for modeling, first determine the number of autoregressive order model using the AIC information criterion of order 5. Then, select the sigma chi square distribution as prior distribution, the normal distribution parameters is selected according to the prior distribution. The likelihood function of the 3.1 and 3.2 sections are given, according to the Bias principle, the third chapter is using the MCMC algorithm based on R language in R2WinBUGS, the Hongkong Hang Seng index points respectively to estimate the parameters of Bias 0.01,0.025 and the 0.05 quantile autoregressive VaR model, the parameters of the posterior density map, dynamic iteration figure GR statistic and convergence graph. Through a series of analysis of the above results show that ALD based Bias quantile autoregressive model VaR and AEPD Bias, based on the quantile autoregressive VaR model Each level under the Markov chain are convergent, and the parameter estimation error is smaller. In addition respectively from the same quantile level compared with different lag variables influence the VaR value, and from different levels the same lag variable effect on VaR values. According to the above construction the model can calculate different confidence levels (into different levels respectively) under the Hongkong Hang Seng Index VaR value. By comparing the actual value of VaR and VaR estimates, the actual value is less than the most VaR VaR estimates, that most of the losses in the forecasting model. At the same time by estimating the ratio within different confidence levels VaR and VaR values showed that the higher the level of confidence, the more conservative estimates, the actual value of the possibility of more than the predicted value is smaller. In the fifth chapter, the application of Kupiec failure rate test method, the fourth chapter of the ALD based on a number of points from Bias The VaR regression model and AEPD Bias quantile evaluation model based on VaR regression. Through the failure interval, the number of failure, the failure rate, LR value and LR value to compare the two models, the results show that the VaR model based on VaR model of AEPD based on ALD failure number less, less failure and the VaR rate. VaR AEPD model and calculation of the traditional historical simulation method based on the comparison. The results showed that the better effect of VaR model based on AEPD. Finally in the sixth chapter, a summary and outlook.

【學(xué)位授予單位】：南京財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F832.51;F224
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本文編號：1599053