金融波动率的非线性分析及其应用
发布时间：2018-11-17 08:07
【摘要】：金融市场波动率的统计特征研究一直是金融领域里一个十分重要的课题。由于金融波动率特殊的研究背景和本身所具有的非线性特征，对它进行估计和预测显得越来越重要。 本文建立了ARFIMA-EGARCH-GED模型(扰动误差服从广义误差分布，thegeneralizederror distribution，GED)，用来分析金融波动率的非对称性和长记忆性这两个非线性特征。在该模型扰动误差服从广义误差分布的条件下，利用极大似然估计方法对模型进行估计，证明了平方误差高阶矩的有界性，得出了极大似然估计量的渐近正态性。 为了分析资产收益波动的“尖峰厚尾”、长记忆性和非对称性特征，，本文提出了ARFIMA-EGARCH-GED波动率模型。以沪深综指为例，在扰动误差分别服从T分布、正态分布和GED分布的前提下进行模型拟合分析，得出ARFIMA-EGARCH-GED模型拟合波动率效果最佳。同EGARCH、FIGARCH模型对比，ARFIMA-EGARCH-GED模型能较好的解决沪深股市收益率波动的“尖峰厚尾”、长记忆性和非对称性特征，且对波动率拟合效果较好，并对波动率作了短期的预测。 鉴于ARFIMA-EGARCH-GED模型对波动率的拟合效果较好，利用模型拟合的波动率来分析波动率和收益率的关系以及不同市场波动率之间的关系。采用局部多项式估计和N-W(Nadaraya-Watson)核估计这两种非参数方法，得出收益率的绝对值越大，波动率越大；收益率为零时，波动率最小。沪深两市波动率之间整体存在正相关，局部存在负相关。局部多项式估计优于N-W核估计。
[Abstract]:The study of the statistical characteristics of volatility in financial markets has been a very important subject in the field of finance. Because of the special research background and nonlinear characteristics of financial volatility, it is more and more important to estimate and predict financial volatility. In this paper, the ARFIMA-EGARCH-GED model (generalized error distribution of disturbance error, thegeneralizederror distribution,GED) is established to analyze the asymmetric and long memory characteristics of financial volatility. Under the condition that the model perturbs the generalized error distribution, the maximum likelihood estimation method is used to estimate the model. The boundedness of the high-order moments of the square error is proved, and the asymptotic normality of the maximum likelihood estimator is obtained. In order to analyze the "peak and thick tail", long memory and asymmetric characteristics of asset return volatility, a ARFIMA-EGARCH-GED volatility model is proposed in this paper. Taking Shanghai and Shenzhen Composite Index as an example, under the premise of T distribution, normal distribution and GED distribution respectively, the model fitting analysis is carried out, and the result of ARFIMA-EGARCH-GED model fitting volatility is the best. Compared with the EGARCH,FIGARCH model, the ARFIMA-EGARCH-GED model can solve the "peak and thick tail", long memory and asymmetric characteristics of the volatility of Shanghai and Shenzhen stock market, and the effect of the volatility fitting is better, and the volatility is predicted in the short term. In view of the good fitting effect of ARFIMA-EGARCH-GED model on volatility, the relationship between volatility and yield and the relationship between volatility and market volatility are analyzed by using the volatility fitted by the model. Two nonparametric methods, local polynomial estimation and N-W (Nadaraya-Watson) kernel estimation, are used to obtain that the higher the absolute value of the yield is, the greater the volatility is, and the less the volatility is when the return rate is 00:00. The volatility of Shanghai and Shenzhen stock markets has positive correlation and negative correlation. Local polynomial estimation is superior to N-W kernel estimation.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;O212.1;F832.51
本文编号：2337077
[Abstract]:The study of the statistical characteristics of volatility in financial markets has been a very important subject in the field of finance. Because of the special research background and nonlinear characteristics of financial volatility, it is more and more important to estimate and predict financial volatility. In this paper, the ARFIMA-EGARCH-GED model (generalized error distribution of disturbance error, thegeneralizederror distribution,GED) is established to analyze the asymmetric and long memory characteristics of financial volatility. Under the condition that the model perturbs the generalized error distribution, the maximum likelihood estimation method is used to estimate the model. The boundedness of the high-order moments of the square error is proved, and the asymptotic normality of the maximum likelihood estimator is obtained. In order to analyze the "peak and thick tail", long memory and asymmetric characteristics of asset return volatility, a ARFIMA-EGARCH-GED volatility model is proposed in this paper. Taking Shanghai and Shenzhen Composite Index as an example, under the premise of T distribution, normal distribution and GED distribution respectively, the model fitting analysis is carried out, and the result of ARFIMA-EGARCH-GED model fitting volatility is the best. Compared with the EGARCH,FIGARCH model, the ARFIMA-EGARCH-GED model can solve the "peak and thick tail", long memory and asymmetric characteristics of the volatility of Shanghai and Shenzhen stock market, and the effect of the volatility fitting is better, and the volatility is predicted in the short term. In view of the good fitting effect of ARFIMA-EGARCH-GED model on volatility, the relationship between volatility and yield and the relationship between volatility and market volatility are analyzed by using the volatility fitted by the model. Two nonparametric methods, local polynomial estimation and N-W (Nadaraya-Watson) kernel estimation, are used to obtain that the higher the absolute value of the yield is, the greater the volatility is, and the less the volatility is when the return rate is 00:00. The volatility of Shanghai and Shenzhen stock markets has positive correlation and negative correlation. Local polynomial estimation is superior to N-W kernel estimation.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;O212.1;F832.51
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