摘要
最近的研究表明，若要限制氣候變化，相對於其他溫室氣體或空氣汙染物而言，更應側重於減少二氧化碳的排放。許多國家都非常重視碳排放，以改善空氣質量和公共健康。歐洲和其他一些國家的人類活動產生的碳排放的最大來源是為產生電力，熱力和動力而進行的化石燃料的燃燒。化石燃料和碳排放的價格可能會相互影響。由於碳排放的重要性及其與化石燃料的聯繫，以及格蘭傑（1980）在炭排放，原油和煤炭現貨和期貨價格，回報率，波動率上的可能性，這個領域近來已成為非常重要的研究課題。對美國而言，原油和煤炭的日均現貨價格和期貨價格可用，但沒有每日碳排放價格的期貨價格。對於歐盟而言，目前沒有煤炭或碳排放的每日現貨價格，但有原油，煤炭和碳排放的每日期貨價格。因此，每日價格將用於分析碳排放，原油和煤炭的現貨價格和期貨價格的格蘭傑因果關係和波動溢出效應。由於估計量是基於正態分佈的錯誤假設下的QMLE，我們將似然比（LR）檢驗改為準似然比檢驗（QLR）以測試多變量條件波動率對角BEKK模型，該模型估計和檢驗波動率溢出效應，並且具有有效的規律性條件和漸近性質，全BEKK模型也可以估計波動溢出效應，但是只有在零非對角線元素的零假設下才具有有效的正則性條件和漸近性質。建議使用最佳套期保值比率的動態套期保值策略來分析現貨和期貨收益的市場波動以及碳排放，原油和煤炭價格的波動。

Abstract
Recent research shows that efforts to limit climate change should focus on reducing emissions of carbon dioxide over other greenhouse gases or air pollutants. Many countries are paying substantial attention to carbon emissions to improve air quality and public health. The largest source of carbon emissions from human activities in some countries in Europe and elsewhere is from burning fossil fuels for electricity, heat, and transportation. The prices of fuel and carbon emissions can influence each other. Owing to the importance of carbon emissions and their connection to fossil fuels, and the possibility of Granger (1980) causality in spot and futures prices, returns and volatility of carbon emissions, crude oil and coal have recently become very important research topics. For the USA, daily spot and futures prices are available for crude oil and coal, but there are no daily futures prices for carbon emissions. For the EU, there are no daily spot prices for coal or carbon emissions, but there are daily futures prices for crude oil, coal and carbon emissions. For this reason, daily prices will be used to analyse Granger causality and volatility spillovers in spot and futures prices of carbon emissions, crude oil, and coal. As the estimators are based on QMLE under the incorrect assumption of a normal distribution, we modify the likelihood ratio (LR) test to a quasi-likelihood ratio test (QLR) to test the multivariate conditional volatility Diagonal BEKK model, which estimates and tests volatility spillovers, and has valid regularity conditions and asymptotic properties, against the alternative Full BEKK model, which also estimates volatility spillovers, but has valid regularity conditions and asymptotic properties only under the null hypothesis of zero off-diagonal elements. Dynamic hedging strategies using optimal hedge ratios are suggested to analyse market fluctuations in the spot and futures returns and volatility of carbon emissions, crude oil and coal prices.

Contents
1. Introduction...................................................................................................................... 4
2. Data .................................................................................................................................. 5
3. Methodology .................................................................................................................. 10
3.1 Univariate Conditional Volatility ......................................................................... 11
3.2 Multivariate Conditional Volatility ...................................................................... 13
3.3 Diagonal BEKK ..................................................................................................... 14
3.4 Full, Triangular and Hadamard BEKK .................................................................... 15
3.5 Granger Causality, Volatility Spillovers, and Optimal Hedge Ratios ..................... 17
4. Unit Root Tests ............................................................................................................... 22
5. Granger Causality and Spillovers in Returns and Volatilities........................................... 23
6. Concluding Remarks ....................................................................................................... 27
References .......................................................................................................................... 50

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