国际碳排放持有成本的N因素仿射模型

An N-Factor Affine Model of Cost-Of-Carry for International Carbon Emissions

在延伸Cortazar和王苏生的N因素仿射模型基础上,假设多元不可观察的状态变量服从均值回复过程,我们构建一个新的碳排放持有成本N因素仿射模型。基于ICE和BLUENEXT交易所期货和现货的价差作为碳排放持有成本,作者运用卡尔曼滤波和最大似然法对碳排放持有成本仿射模型进行模拟分析。实证结果显示,碳排放持有成本表现出明显的均值回复过程,除了市场风险溢价,各状态变量的均值回复速度、方差和协方差均在5%显著水平下表现出较高的显著性。通过平均绝对误差(MAE)和均方根误差(RMSE)方法对三因素碳排放持有成本仿射模型进行拟合能力评价,模型拟合误差值均显著性低于1%,这充分说明碳排放持有成本仿射模型具有较好的拟合能力,三因素仿射模型能够较准确地模拟和预测碳排放持有成本。

In recent years,issues related to CO2 gas emissions have attracted public attention.CO2 gas emission controlling and environment protection have become hot political and academic topics.Since the launch of European Union emissions trading scheme （EU ETS） in 2005,CO2 emissions allowance has become valuable commodity which can be transferred and exchanged in the CO2 emissions allowances market.China is now actively exploring and developing emission trading scheme in the future.Chinese market participants,such as enterprises,financial institutes,hedgers,and investors,are lack of the capability of hedging and risk management in the asset portfolio for carbon emissions.Carbon emissions market is an emerging financial market.Spot price and futures price for carbon emission has strong time-varying property.On the basis of historical trading data of cost-of-carry for carbon emission,examining mean-reversion process and accurately grasping the term structure of cost-of-carry are not only an important way for market participants to achieve market arbitrage in the spot and futures markets,but also an important management tool for market participants to optimize the assets portfolio and strengthen risk management.Government regulation policy,energy utilization efficiency,and promotion decision in low-carbon technology have driven long-run quantity of demand and supply in the carbon emissions market,and directly promoted long-term price trend for both spot and futures carbon emissions.The change of interest rate,extreme climate and energy price volatility have caused the short-run shock of expected total quantity of demand and supply in the carbon emissions market,and directly affected short-term price fluctuation for carbon emission.Based on the assumption that multivariate unobservable state variables follow mean-reverting process,we propose a new Nfactor affine model of cost-of-carry for carbon emissions to extend N-factor affine model proposed by the Cortazar and Wang.The parameters coefficients of affinity model are estimated by using cost-of-carry with different maturities extended from the prices spread between spot and futures for carbon emissions.Measurement and transition equations are used as observable variables.We provide empirical evidence of three-factor affine model of cost-of carry for carbon emissions by using Kalman filter and likelihood methods.Our empirical results show that cost-of-carry for carbon emissions has mean-reversion process.Mean-reverting speeds,volatility and covariance among the state variables are highly significant at the confidence level of 5％,while market risk premium is not significant to affect cost-of-carry for carbon emissions.Affine model robustness of cost-of-carry for carbon emissions is evaluated by using mean absolute errors （MAE） and root mean square errors （RMSE）.The fitting errors of affine model are significantly less than 1％,and these signs fully show better robustness of three-factor affine model of cost-of-carry for carbon emissions.