贝叶斯分位数自回归方法的研究及在香港恒生指数风险测度上的应用

发布时间：2018-03-11 16:52

  本文选题：非对称拉普拉斯分布　切入点：非对称指数幂分布　出处：《南京财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：贝叶斯分位数回归方法是近年来国内外的研究热点,把贝叶斯分位数回归方法应用于金融风险测度是一个重要的研究课题,而计算风险价值VaR是金融市场风险测度的主流方法.本文探讨基于贝叶斯分位数自回归方法的VaR建模,并用该方法研究香港恒生指数的VaR风险测度.第一章阐述了选题的背景以及研究意义,并进行了国内外文献综述.第二章是基本概念及其方法的简要概述,包括：分位数回归,贝叶斯分析的相关理论和方法,以及VaR的概念与主要性质.第三章从理论上构建了基于贝叶斯分位数自回归的VaR建模框架.本章分成两大部分.第一部分,分别针对误差项服从非对称拉普拉斯分布(ALD)和误差项服从非对称指数幂分布(AEPD)的分位数回归模型,通过设定参数的先验分布及确定样本的似然函数,根据贝叶斯原理,利用MCMC中算法按照参数的满条件后验分布交替采样,得到具有平稳分布的马氏链的一个样本实现,该平稳分布就是参数的后验分布.由于均方误差损失下,参数的最优贝叶斯估计就是其后验均值,所以可以用马氏链的样本均值作为参数的最优估计.值得说明的是：由于ALD和AEPD都是非标准分布,所以在采样前,本文对它们的似然函数进行了变换.第二部分,作为上述贝叶斯分位数回归模型的一种特殊类型,遵循上述思路,构建了贝叶斯分位数自回归VaR模型,具体做法是：在提出了分位数自回归VaR模型之后,按照AIC信息选择准则给出此模型的定阶方法,利用第一部分给出的方法对参数进行贝叶斯估计,并给出不同分位水平下VaR模型的评价方法.第四章是在第三章给出的理论建模框架的基础上,将贝叶斯分位数自回归VaR模型应用于香港恒生指数的风险测度中.选取香港恒生指数2010年1月4日到2014年1月10日收盘价,通过对数变换后获得对数收益率数据,再从均值、标准差、偏度、峰度、JB统计量、ADF值、自相关系数与偏相关系数几个方面,对这些数据进行特征分析后,发现了数据具有非正态性、尖峰厚尾性、平稳性和自相关性,因而能确定本章模型类型隶属于第三章的贝叶斯分位数自回归VaR模型.根据第三章构建的理论建模框架,首先应用AIC信息准则确定模型的自回归阶数为5阶.然后,选取卡方分布为σ的先验分布,其余参数则选取正态分布为先验分布,按照3.1节和3.2节给出的似然函数,根据贝叶斯原理,利用第三章给出的MCMC算法结合R语言中的R2WinBUGS,得到了香港恒生指数分位水平分别为0.01、0.025与0.05的贝叶斯分位数自回归VaR模型的参数估计、各个参数的后验密度图、动态迭代图以及GR统计量收敛性图.通过对上述结果的一系列分析表明：基于ALD的贝叶斯分位数自回归VaR模型和基于AEPD的贝叶斯分位数自回归VaR模型的各个分位水平下的马氏链均是收敛的,且参数估计的误差较小.此外分别从同一分位水平角度比较了不同滞后期的自变量对VaR值的影响,以及从不同分位水平下同一滞后期的自变量对VaR值的影响.根据上述所建的模型可以计算不同置信水平(分别对应不同的分位水平)下的香港恒生指数的VaR值.通过比较VaR实际值和VaR估计值,可知大部分VaR实际值小于VaR估计值,说明大部分损失在模型预测之内.同时通过比不同置信水平的VaR实际值和VaR估计值可知,置信水平越高,估计越保守,实际值超过预测值的可能性越小.第五章应用Kupiec失败率检验法,对第四章所建的基于ALD的贝叶斯分位数自回归VaR模型和基于AEPD的贝叶斯分位数自回归VaR模型进行效果评价.通过得到的失败区间、失败数、失败率、LR值以及LR临界值来比较两个模型,结果表明：基于AEPD的VaR模型比基于ALD的VaR模型的失败数更少,失败率更小.并把基于AEPD的VaR模型与计算VaR的传统的历史模拟法进行比较.结果发现基于AEPD的VaR模型效果更好.最后在第六章,对全文进行了总结与展望.
[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.

【学位授予单位】：南京财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51;F224
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本文编号：1599053