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題名 碳排放權衍生性商品訂價與實證分析：均數復歸、隨機波動度與跳躍風險
Derivative Pricing and Empirical Analysis in CO2 Emission Allowance: Mean Reversion, Stochastic Volatility, and Jump Risks
作者 陳亭甫
Chen, Ting Fu
貢獻者 林士貴
Lin, Shih Kuei
陳亭甫
Chen, Ting Fu
關鍵詞 碳排放權
均數復歸
隨機波動度
跳躍風險
共同估計
Emission Allowance
Mean-Reversion
Stochastic Volatility
Jump Risks
Joint Estimation
日期 2016
上傳時間 14-Nov-2016 16:10:06 (UTC+8)
摘要 溫室氣體的減量已成為全球各國必須共同面對的課題，歐盟委員會為幫助其成員國達成減排目標，於 2005 年成立歐盟碳排放交易體系，使得碳排放權成為可以具體交易的商品。為了更加了解碳排放市場特性以增進風險管理績效，本研究可分為以下各個面向：第一，在財務定價模型方面，本研究同時採用過去文獻針對商品資產所使用的隨機波動度、均數復歸、價格跳躍與波動度跳躍特性，並發展粒子濾波方法與最大期望演算法作為模型參數估計方法。第二，透過Esscher轉換推導風險中立下的價格動態，並藉由傅利葉轉換的評價方法推導出各個模型所對應的期貨選擇權評價公式。第三，延續本文採用的碳權價格動態模型下，以歐洲碳排放許可憑證(EUA)為標的商品，進行歐盟碳排放交易體系在第三階段的市場實證研究。本文實證研究結果發現，均數復歸、隨機波動度以及價格與波動度相關跳躍模型，確實存在於EUA市場中，無論在現貨市場或選擇權市場都是重要的價格因素。分析EUA市場特性時，應採用同時考量現貨市場與衍生性商品市場價格的共同估計方法，才能夠完整的反映出EUA市場的價格特性。
Reducing the emission of greenhouse gases has become a major task for countries all over the world. To help the member states achieve the reduction target, EU emissions trading system (EU ETS) is constructed by European Commission, so that the emission allowance becomes a tradable commodity. To investigate the features of the price dynamics in the carbon market and to enhance the performance of risk management, this study is constructed as follows: First, the stylized facts including mean-reversion, stochastic volatility, price jumps, and volatility jumps, which are documented in the literature on modeling dynamics of commodities, are employed to construct the pricing model. The particle filter procedure and the expectation-maximization algorithm are developed to estimate the proposed models. Second, the pricing models under the risk-neutral measure are obtained through the Esscher transform, and the analytic pricing formula for the option on futures is derived by means of Fourier transform. Third, the EU ETS in Phase III is investigated through the price of EU allowances (EUA), which is the underlying of the EU ETS. The empirical findings show the existence of the mean-reversion, stochastic volatility, and correlated jumps risks in the EUA price dynamics, and these stylized facts are crucial factors in fitting the EUA price dynamics in both spot market and option market. When analyzing the features of the EUA market, the joint estimation, which involves the information contained in both spot and derivatives markets, should be adopted to obtain the comprehensive stylized facts of the EUA price dynamics.
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Bakshi, G., C. Cao, and Z. W. Chen (1997). "Empirical Performance of Alternative Option Pricing Models." Journal of Finance 52(5): 2003-2049.
Bakshi, G. and L. Wu (2010). "The Behavior of Risk and Market Prices of Risk over the Nasdaq Bubble Period." Management Science 56(12): 2251-2264.
Bates, D. (1996). "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options." Review of Financial Studies 9(1): 69-107.
Benz, E. and S. Trück (2009). "Modeling the Price Dynamics of CO2 Emission Allowances." Energy Economics 31(1): 4-15.
Bredin, D. and C. Muckley (2011). "An Emerging Equilibrium in the EU Emissions Trading Scheme." Energy Economics 33(2): 353-362.
Breeden, D. T. (1979). "An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities." Journal of Financial Economics 7(3): 265-296.
Broadie, M., M. Chernov, and M. Johannes (2007). "Model Specification and Risk Premia: Evidence from Futures Options." The Journal of Finance 62(3): 1453-1490.
Brooks, C. and M. Prokopczuk (2013). "The Dynamics of Commodity Prices." Quantitative Finance 13(4): 527-542.
Carmona, R. and J. Hinz (2011). "Risk-Neutral Models for Emission Allowance Prices and Option Valuation." Management Science 57(8): 1453-1468.
Çetin, U. and M. Vweschuere (2009). "Pricing and Hedging in Carbon Emissions Markets." International Journal of Theoretical and Applied Finance 12(7): 949-967.
Chang, J. R., M. W. Hung, C. F. Lee, and H. M. Lu (2007). "The Jump Behavior of Foreign Exchange Market: Analysis of Thai Baht." Review of Pacific Basin Financial Markets and Policies 10(2): 265-288.
Chesney, M. and L. Taschini (2012). "The Endogenous Price Dynamics of Emission Allowances and an Application to CO2 Option Pricing." Applied Mathematical Finance 19(5): 447-475.
Chevallier, J. (2009). "Carbon Futures and Macroeconomic Risk Factors: A View from the EU ETS." Energy Economics 31(4), 614-625
Chevallier, J. (2010). "Carbon Prices during the EU ETS Phase II: Dynamics and Volume Analysis." HAL.
Christoffersen, P., K. Jacobs, and K. Mimouni (2010). "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices." Review of Financial Studies 23(8): 3141-3189.
Conrad, C., D. Rittler, and W. Rotfuss (2012). "Modeling and Explaining the Dynamics of European Union Allowance Prices at High-frequency." Energy Economics 34(1): 316-326.
Cox, J. C., J. E. Ingersoll, and S. A. Ross (1985). "A Theory of the Term Structure of Interest Rates." Econometrica 53(2): 385-408.
Cronshaw, M. B. and J. B. Kruse (1996). "Regulated Firms in Pollution Permit Markets with Banking." Journal of Regulatory Economics 9(2): 179-189.
Daskalakis, G., D. Psychoyios, and R. N. Markellos (2009). "Modeling CO2 Emission Allowance Prices and Derivatives: Evidence from the European Trading Scheme." Journal of Banking & Finance 33(7): 1230-1241.
De Perthuis, C. and R. Trotignon (2014). "Governance of CO2 Markets: Lessons from the EU ETS." Energy Policy 75: 100-106.
Diewald, L., M. Prokopczuk, and C. W. Simen (2015). "Time-Variations in Commodity Price Jumps." Journal of Empirical Finance 31: 72-84.
Duffie, D., J. Pan, and K. Singleton (2000). "Transform Analysis and Asset Pricing for Affine Jump-Diffusions." Econometrica 68(6): 1343-1376.
Elliott, R. J., L. Chan, and T. K. Siu (2005). "Option Pricing and Esscher Transform under Regime Switching" Annals of Finance 1(4): 423-432.
Engle, R. F. and V. K. Ng (1993). "Measuring and Testing the Impact of News on Volatility." The Journal of Finance 48(5): 1749-1778.
Esscher, F. (1932). "On the Probability Function in the Collective Theory of Risk." Skandinavisk Aktuarietidskrift 15(3): 175-195.
Eraker, B., M. Johannes, and N. Polson (2003). "The Impact of Jumps in Volatility and Returns." The Journal of Finance 58(3): 1269-1300.
Gerber, H. U. (1974). "On Additive Premium Calculation Principles." ASTIN Bulletin 7(3): 215-222.
Gerber, H. U., E. S. W. Shiu (1994). "Option Pricing by Esscher Transforms." Transactions of Society of Actuaries 46: 99-140.
Godsill, S., A. Doucet, and M. West (2004). "Monte Carlo Smoothing for Non-Linear Time Series." Journal of the Acoustical Society of America 99(465): 156-168.
Goovaerts, M. J., F. De Vijlder, and J. Haezendonck (1984). "Insurance Premiums." North Holland Publishing, Amsterdam.
Goovaerts, M. J., R. J. A. Laeven (2008). "Actuarial Risk Measures for Financial Derivative Pricing." Insurance: Mathematics and Economics 42(2): 540-547.
Heston, S. L. (1993). "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options." Review of Financial Studies 6(2): 327-343.
Hilliard, J. E. and J. Reis (1998). "Valuation of Commodity Futures and Options Under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot." The Journal of Financial and Quantitative Analysis 33(1): 61-86.
Hintermann, B. (2010). "Allowance Price Drivers in the First Phase of the EU ETS." Journal of Environmental Economics and Management 59(1): 43-56.
Hu, F. and J. V. Zidek (2002). "The Weighted Likelihood." Canadian Journal of Statistics 30(3): 347-371.
Johannes, M. S., N. G. Polson, and J. R. Stroud (2009). "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices." Review of Financial Studies 22(7): 2759-2799.
Kaeck, A. and C. Alexander (2013). "Stochastic Volatility Jump-Diffusions for European Equity Index Dynamics." European Financial Management 19(3): 470-496.
Kitagawa, G. and S. Sato (2001). "Monte Carlo Smoothing and Self-Organising State-Space Model, Sequential Monte Carlo Methods in Practice, 177-195. Springer-Verlag, NY.

Koch, N., S. Fuss, G. Grosjean, and O. Edenhofer (2014). "Causes of the EU ETS Price Drop: Recession, CDM, Renewable Policies or A Bit of Everything?-New Evidence." Energy Policy 73: 676-685.
Kou, S., C. Yu, and H. Zhong (2016). "Jumps in Equity Index Returns Before and During the Recent Financial Crisis: A Bayesian Analysis." Management Science.
Lopes, H. F. and R. S. Tsay (2011). "Particle Filters and Bayesian Inference in Financial Econometrics." Journal of Forecasting 30(1): 168-209.
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描述 博士
國立政治大學
金融學系
99352504
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0993525043
資料類型 thesis
dc.contributor.advisor 林士貴zh_TW
dc.contributor.advisor Lin, Shih Kueien_US
dc.contributor.author (Authors) 陳亭甫zh_TW
dc.contributor.author (Authors) Chen, Ting Fuen_US
dc.creator (作者) 陳亭甫zh_TW
dc.creator (作者) Chen, Ting Fuen_US
dc.date (日期) 2016en_US
dc.date.accessioned 14-Nov-2016 16:10:06 (UTC+8)-
dc.date.available 14-Nov-2016 16:10:06 (UTC+8)-
dc.date.issued (上傳時間) 14-Nov-2016 16:10:06 (UTC+8)-
dc.identifier (Other Identifiers) G0993525043en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/103980-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融學系zh_TW
dc.description (描述) 99352504zh_TW
dc.description.abstract (摘要) 溫室氣體的減量已成為全球各國必須共同面對的課題，歐盟委員會為幫助其成員國達成減排目標，於 2005 年成立歐盟碳排放交易體系，使得碳排放權成為可以具體交易的商品。為了更加了解碳排放市場特性以增進風險管理績效，本研究可分為以下各個面向：第一，在財務定價模型方面，本研究同時採用過去文獻針對商品資產所使用的隨機波動度、均數復歸、價格跳躍與波動度跳躍特性，並發展粒子濾波方法與最大期望演算法作為模型參數估計方法。第二，透過Esscher轉換推導風險中立下的價格動態，並藉由傅利葉轉換的評價方法推導出各個模型所對應的期貨選擇權評價公式。第三，延續本文採用的碳權價格動態模型下，以歐洲碳排放許可憑證(EUA)為標的商品，進行歐盟碳排放交易體系在第三階段的市場實證研究。本文實證研究結果發現，均數復歸、隨機波動度以及價格與波動度相關跳躍模型，確實存在於EUA市場中，無論在現貨市場或選擇權市場都是重要的價格因素。分析EUA市場特性時，應採用同時考量現貨市場與衍生性商品市場價格的共同估計方法，才能夠完整的反映出EUA市場的價格特性。zh_TW
dc.description.abstract (摘要) Reducing the emission of greenhouse gases has become a major task for countries all over the world. To help the member states achieve the reduction target, EU emissions trading system (EU ETS) is constructed by European Commission, so that the emission allowance becomes a tradable commodity. To investigate the features of the price dynamics in the carbon market and to enhance the performance of risk management, this study is constructed as follows: First, the stylized facts including mean-reversion, stochastic volatility, price jumps, and volatility jumps, which are documented in the literature on modeling dynamics of commodities, are employed to construct the pricing model. The particle filter procedure and the expectation-maximization algorithm are developed to estimate the proposed models. Second, the pricing models under the risk-neutral measure are obtained through the Esscher transform, and the analytic pricing formula for the option on futures is derived by means of Fourier transform. Third, the EU ETS in Phase III is investigated through the price of EU allowances (EUA), which is the underlying of the EU ETS. The empirical findings show the existence of the mean-reversion, stochastic volatility, and correlated jumps risks in the EUA price dynamics, and these stylized facts are crucial factors in fitting the EUA price dynamics in both spot market and option market. When analyzing the features of the EUA market, the joint estimation, which involves the information contained in both spot and derivatives markets, should be adopted to obtain the comprehensive stylized facts of the EUA price dynamics.en_US
dc.description.tableofcontents 1. Introduction 1
1.1 Greenhouse gas and the Kyoto protocol 1
1.2 EU emission trading scheme (EU ETS) 3
1.3 The characters of carbon price in the EU ETS 7
2. The Models and the Method of Estimation 17
2.1 The pricing models 17
2.2 The particle filter and EM algorithm 19
3. The Pricing Formula 27
3.1 The pricing kernels 27
3.2 Fourier transform pricing scheme for options on futures 36
4. Empirical Analysis in the EU ETS Phase III 43
4.1 Data description 43
4.2 Model estimation 46
4.3 Option pricing errors of alternative pricing models 56
4.4 Joint estimation 63
5. Conclusions 71
References 74
Appendix 79
A. The pseudo code of PF and EM algorithm for parameter estimation 79
B. The proof of Proposition 2 80
C. The proof of Proposition 4 83		zh_TW
dc.format.extent 2842356 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0993525043en_US
dc.subject (關鍵詞) 碳排放權zh_TW
dc.subject (關鍵詞) 均數復歸zh_TW
dc.subject (關鍵詞) 隨機波動度zh_TW
dc.subject (關鍵詞) 跳躍風險zh_TW
dc.subject (關鍵詞) 共同估計zh_TW
dc.subject (關鍵詞) Emission Allowanceen_US
dc.subject (關鍵詞) Mean-Reversionen_US
dc.subject (關鍵詞) Stochastic Volatilityen_US
dc.subject (關鍵詞) Jump Risksen_US
dc.subject (關鍵詞) Joint Estimationen_US
dc.title (題名) 碳排放權衍生性商品訂價與實證分析：均數復歸、隨機波動度與跳躍風險zh_TW
dc.title (題名) Derivative Pricing and Empirical Analysis in CO2 Emission Allowance: Mean Reversion, Stochastic Volatility, and Jump Risksen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Asselta, H. V. and T. Brewer (2010). "Addressing Competitiveness and Leakage Concerns in Climate Policy: An Analysis of Border Adjustment Measures in the US and the EU." Energy Policy 38(1): 42-51.
Bakshi, G., C. Cao, and Z. W. Chen (1997). "Empirical Performance of Alternative Option Pricing Models." Journal of Finance 52(5): 2003-2049.
Bakshi, G. and L. Wu (2010). "The Behavior of Risk and Market Prices of Risk over the Nasdaq Bubble Period." Management Science 56(12): 2251-2264.
Bates, D. (1996). "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options." Review of Financial Studies 9(1): 69-107.
Benz, E. and S. Trück (2009). "Modeling the Price Dynamics of CO2 Emission Allowances." Energy Economics 31(1): 4-15.
Bredin, D. and C. Muckley (2011). "An Emerging Equilibrium in the EU Emissions Trading Scheme." Energy Economics 33(2): 353-362.
Breeden, D. T. (1979). "An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities." Journal of Financial Economics 7(3): 265-296.
Broadie, M., M. Chernov, and M. Johannes (2007). "Model Specification and Risk Premia: Evidence from Futures Options." The Journal of Finance 62(3): 1453-1490.
Brooks, C. and M. Prokopczuk (2013). "The Dynamics of Commodity Prices." Quantitative Finance 13(4): 527-542.
Carmona, R. and J. Hinz (2011). "Risk-Neutral Models for Emission Allowance Prices and Option Valuation." Management Science 57(8): 1453-1468.
Çetin, U. and M. Vweschuere (2009). "Pricing and Hedging in Carbon Emissions Markets." International Journal of Theoretical and Applied Finance 12(7): 949-967.
Chang, J. R., M. W. Hung, C. F. Lee, and H. M. Lu (2007). "The Jump Behavior of Foreign Exchange Market: Analysis of Thai Baht." Review of Pacific Basin Financial Markets and Policies 10(2): 265-288.
Chesney, M. and L. Taschini (2012). "The Endogenous Price Dynamics of Emission Allowances and an Application to CO2 Option Pricing." Applied Mathematical Finance 19(5): 447-475.
Chevallier, J. (2009). "Carbon Futures and Macroeconomic Risk Factors: A View from the EU ETS." Energy Economics 31(4), 614-625
Chevallier, J. (2010). "Carbon Prices during the EU ETS Phase II: Dynamics and Volume Analysis." HAL.
Christoffersen, P., K. Jacobs, and K. Mimouni (2010). "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices." Review of Financial Studies 23(8): 3141-3189.
Conrad, C., D. Rittler, and W. Rotfuss (2012). "Modeling and Explaining the Dynamics of European Union Allowance Prices at High-frequency." Energy Economics 34(1): 316-326.
Cox, J. C., J. E. Ingersoll, and S. A. Ross (1985). "A Theory of the Term Structure of Interest Rates." Econometrica 53(2): 385-408.
Cronshaw, M. B. and J. B. Kruse (1996). "Regulated Firms in Pollution Permit Markets with Banking." Journal of Regulatory Economics 9(2): 179-189.
Daskalakis, G., D. Psychoyios, and R. N. Markellos (2009). "Modeling CO2 Emission Allowance Prices and Derivatives: Evidence from the European Trading Scheme." Journal of Banking & Finance 33(7): 1230-1241.
De Perthuis, C. and R. Trotignon (2014). "Governance of CO2 Markets: Lessons from the EU ETS." Energy Policy 75: 100-106.
Diewald, L., M. Prokopczuk, and C. W. Simen (2015). "Time-Variations in Commodity Price Jumps." Journal of Empirical Finance 31: 72-84.
Duffie, D., J. Pan, and K. Singleton (2000). "Transform Analysis and Asset Pricing for Affine Jump-Diffusions." Econometrica 68(6): 1343-1376.
Elliott, R. J., L. Chan, and T. K. Siu (2005). "Option Pricing and Esscher Transform under Regime Switching" Annals of Finance 1(4): 423-432.
Engle, R. F. and V. K. Ng (1993). "Measuring and Testing the Impact of News on Volatility." The Journal of Finance 48(5): 1749-1778.
Esscher, F. (1932). "On the Probability Function in the Collective Theory of Risk." Skandinavisk Aktuarietidskrift 15(3): 175-195.
Eraker, B., M. Johannes, and N. Polson (2003). "The Impact of Jumps in Volatility and Returns." The Journal of Finance 58(3): 1269-1300.
Gerber, H. U. (1974). "On Additive Premium Calculation Principles." ASTIN Bulletin 7(3): 215-222.
Gerber, H. U., E. S. W. Shiu (1994). "Option Pricing by Esscher Transforms." Transactions of Society of Actuaries 46: 99-140.
Godsill, S., A. Doucet, and M. West (2004). "Monte Carlo Smoothing for Non-Linear Time Series." Journal of the Acoustical Society of America 99(465): 156-168.
Goovaerts, M. J., F. De Vijlder, and J. Haezendonck (1984). "Insurance Premiums." North Holland Publishing, Amsterdam.
Goovaerts, M. J., R. J. A. Laeven (2008). "Actuarial Risk Measures for Financial Derivative Pricing." Insurance: Mathematics and Economics 42(2): 540-547.
Heston, S. L. (1993). "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options." Review of Financial Studies 6(2): 327-343.
Hilliard, J. E. and J. Reis (1998). "Valuation of Commodity Futures and Options Under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot." The Journal of Financial and Quantitative Analysis 33(1): 61-86.
Hintermann, B. (2010). "Allowance Price Drivers in the First Phase of the EU ETS." Journal of Environmental Economics and Management 59(1): 43-56.
Hu, F. and J. V. Zidek (2002). "The Weighted Likelihood." Canadian Journal of Statistics 30(3): 347-371.
Johannes, M. S., N. G. Polson, and J. R. Stroud (2009). "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices." Review of Financial Studies 22(7): 2759-2799.
Kaeck, A. and C. Alexander (2013). "Stochastic Volatility Jump-Diffusions for European Equity Index Dynamics." European Financial Management 19(3): 470-496.
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