碳价格波动率模型构建与预测:基于无穷活动率Levy过程  

Modeling and Predicting the Volatility of Carbon Price:Based on Infinite Activity Levy Processes

作　　者：胡根华 朱福敏[3] HU Gen-hua;ZHU Fu-min(School of Business,Anhui University of Technology,Anhui Maanshan 243032,China;Anhui Institute for Innovation-Driven Development,Anhui Maanshan 243032,China;College of Economics,Shenzhen University,Guangdong Shenzhen 518060,China)

机构地区：[1]安徽工业大学商学院,安徽马鞍山243032 [2]安徽创新驱动发展研究院,安徽马鞍山243032 [3]深圳大学经济学院,广东深圳518060

出　　处：《数理统计与管理》2018年第5期892-903,共12页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(71601125);教育部人文社会科学研究青年基金项目(16YJC790030);教育部人文社会科学研究西部和边疆地区项目(14XJA790002);安徽省自然科学基金项目(1708085QG163);重庆市教委科学技术研究项目(KJ1709236)的资助

摘　　要：考虑碳金融资产价格的跳跃行为特征与杠杆效应,文章选取欧盟碳排放配额现货价格作为研究对象,构建基于无穷活动率Levy过程的碳价格波动率模型并检验其预测效果。首先,假设碳价格不存在跳跃而构建无跳跃的BM-NGARCH模型;然后,假设碳价格的跳跃过程分别服从有限跳跃行为过程与无穷跳跃行为（Variance Gamma过程,Normal Inverse Gaussian过程与Classical Tempered Stable过程）过程,构建MJ-NGARCH模型、VG-NGARCH模型、NIGNGARCH模型和CTS-NGARCH模型等四种Levy波动率模型,并采用基于傅里叶变换的极大似然法估计相关参数;最后,基于上述模型对碳价格进行预测并计算在险价值,进而采用回溯测试方法检验模型的优劣程度。主要研究结果：在5%的显著水平上,BM-NGARCH没有通过尾部检验,而CTS-NGARCH模型在拟合碳价格特征方面具有最佳的拟合效果,说明碳价格存在显著的跳跃行为;在预测方面,BM-NGARCH对碳价格的预测表现最差,而基于无穷活动率Levy过程的碳价格模型都取得较好的预测效果。Taking the jumps and leverage effect in the carbon emission market, this paper is to model the volatility of carbon price based on infinite activity Levy processes, and test the result of forecasting of the model. It selects the daily trading dataset of European Union emission allowance. Firstly, it supposes no jumps in the market and builds the BM-NGARCH. Secondly, it supposes the distributions of jumps satisfying to Merton jump-diffusion process, variance gamma process, normal inverse Gaussian process and classical tempered stable process. And then it builds the MJ-NGARCH model, VG-NGARCH model,NIG-NGARCH model and CTS-NGARCH model, estimates the parameters and fits the models using Maximum Likelihood Estimation based on Fourier transformation. Thirdly, it predicts the carbon prices,computes Value-at-Risk and tests the models by using back-testing method. The empirical study is found that the CTS-NGARCH model is the optimal models among five different Levy-GARCH models,indicating that jumps exist in the carbon emission market. Furthermore, the infinite activity Levy models have nice ability of predicting the carbon prices.

关 键 词：欧盟排放配额 跳跃 LEVY过程 在险价值 回溯测试 

分 类 号：F830.9[经济管理—金融学] O212[理学—概率论与数理统计]