1. NCCU Academic Hub
  2. 學術產出
  3. College of Commerce
  4. Theses
  5. Item

學術產出-Theses

Article View/Open

Publication Export

Google ScholarTM

政大圖書館

Citation Infomation

題名 天氣衍生性商品評價與風險管理：CME雨量指數二元式合約之應用
Valuation and Risk Management of Weather Derivatives: the Application of CME Rainfall Index Binary Contracts
作者 方東杰
Fang, Dong-Jie
貢獻者 林士貴<br>莊明哲
Lin, Shih-Kuei<br>Chuang, Ming-Che
方東杰
Fang, Dong-Jie
關鍵詞 雨量衍生性商品
馬可夫鏈
截斷傅立葉級數
Esscher變換
風險市場價格
Precipitation derivatives
Markov Chain
Truncated fourier series
Esscher transform
Market price of risk
日期 2019
上傳時間 7-Aug-2019 16:13:44 (UTC+8)
摘要 本文討論了CME發行之雨量衍生性商品——雨量指數二元式合約之評價與風險管理。標的之雨量指數由兩種模型所刻畫：以一階兩狀態馬爾可夫鏈建立的發生模型，以及以混合指數分配建立的雨量強度模型。爲了捕捉降雨的季節性特徵，上述兩模型中的參數均以截斷傅立葉級數擬合，其中之係數以最大概似估計法估計，階數根據AIC與BIC判定。在以蒙地卡羅模擬獲得日降雨量模擬路徑後，計算月降雨量並以常態逆高斯分配擬合。鑒於天氣衍生性商品市場之不完備性，本文利用Esscher變換對雨量指數二元式選擇權進行評價，並以CME之真實市場價格校準獲得風險市場價格。最後，利用燃燒分析與敏感度分析討論雨量衍生性商品之風險管理。
In this paper we discuss the valuation and risk management of rainfall index binary contracts, which is a type of precipitation derivatives issued in CME. We describe the underlying rainfall index by occurrence model with first-order, two-state Markov chain, and magnitude model with mixed-exponential distribution. In order to capture the seasonality characteristics of precipitation, the parameters in both models are described with truncated Fourier series, in which the coefficients are fitted by MLE, and the orders are determined by AIC and BIC. We simulate the daily rainfall index by Monte Carlo simulation, and fit the simulated monthly rainfall index with NIG distribution. Since weather derivatives market is an incomplete market, we value the rainfall index binary options by using Esscher transform. The market price of risk is calibrated with real market data from CME. And the risk management of precipitation derivatives is discussed by using burn analysis and sensitivity analysis.
參考文獻 [1] Aanderud, W. G., 1982, “Federal Crop Insurance”, Economics Commentator, Vol. 178, 1-3.
[2] Alexandridis, A. K., Zapranis, A. D., Weather Derivatives: Modeling and Pricing Weather-Related Risk, New York: Springer.
[3] Benth, F.E., Persio, L.D., and Lavagnini, S., 2018, “Stochastic Modeling of Wind Derivatives in Energy Markets”, Risks, Vol.6 (2), 1-21.
[4] Benth, F.E., Šaltytė-Benth, J., and Koekebakker, S., 2007, “Putting A Price on Temperature”, Scandinavian Journal of Statistics, Vol. 34, 746-767.
[5] Benth, F. E., Šaltytė-Benth, J., 2012, Modeling and Pricing in Financial Markets for Weather Derivatives, Singapore: World Scientific.
[6] Bowe, R., Hertzler, G., and Barnett, R. et al., 2003, “Final Report: Multi Peril Crop Insurance Task Force”, Report to the Minister for Agriculture, Forestry and Fisheries.
[7] Brockett, P.L., Wang, M., Yang, C., and Zou, H., 2006, “Portfolio Effects and Valuation of Weather Derivatives”, The Financial Review, Vol. 41 (1), 55-76.
[8] Bühlmann, H., 1980, “An Economic Premium Principle”, Astin Bulletin, Vol. 11, 52-60.
[9] Cabrera, B.L., Odening, M., and Ritter, M., 2013, “Pricing Rainfall Futures at the CME”, Journal of Banking & Finance, Vol.37, 4286-4298.
[10] Cao, M., Li, A., and Wei, J., 2004, “Precipitation Modeling and Contract Valuation: A Frontier in Weather Derivatives”, The Journal of Alternative Investments, Vol.7, 93-99.
[11] Carmona, R., Diko, P., 2004, “Pricing Precipitation Based Derivatives”, International Journal of Theoretical and Applied Finance, Vol. 8 (7), 959-988.
[12] Chen, Y., 2016, “Analysis and Enlightenment of Agricultural System in France, India and Japan”, World Agriculture, Vol. 7, 188-191.
[13] Chite, R. M., 2014, “The 2014 Farm Bill (P.L. 113-79): Summary and Side-by-Side”, Congressional Research Service: http://nationalaglawcenter.org/wp-content/uploads/assets/crs/R43076.pdf
[14] Cramer, S., Kampouridis, M., Freitas, A.A., and Alexandridis, A.K., 2017, “An extensive evaluation of seven machine learning methods for rainfall prediction in weather derivatives”, Expert Systems with Applications, Vol. 85, 169-181.
[15] Dischel, R. S., 1998, “The Fledgling Weather Market Takes Off”, Applied Derivatives Trading Focus, http://www.adtrading.com.
[16] Dorfleitner, G., Wimmer, M, 2010, “The Pricing of Temperature Futures at the Chicago Mercantile Exchange”, Journal of Banking & Finance, Vol. 34 (6), 1360-1370.
[17] Esscher, F., 1932, “On the Probability Function in the Collective Theory of Risk”, Scandinavian Actuarial Journal, Vol. 15, 175-195.
[18] Frittelli, M., 2000, “The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets”, Mathematical Finance, Vol. 10, 39-52.
[19] Halcrow, H. G., 1949, “Actuarial Structures for Crop Insurance”, Journal of Farm Economics, Vol. 31, 418-443.
[20] Härdle, W.K., Osipenko, M., 2017, “A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk”, International Journal of Financial Studies, Vol. 5(4), 1-18.
[21] Hatt, M., Heyhoe, E., and Whittle, L., 2012, “Options for Insuring Australian Agriculture”, ABARES report to client prepared for Climate Division, the Department of Agriculture, Fisheries and Forestry.
[22] Hazell, P., Anderson, J., Balzer, N., Clemmensen, A. H., Hess, U. and Rispoli, F., 2010, “The Potential for Scale and Sustainability in Weather Index Insurance for Agriculture and Rural Livelihoods”, International Fund for Agricultural Development and World Food Programme.
[23] Hazell, P., Skees, J. R., 2006, “Insuring against Bad Weather: Recent Thinking”, India in a Globalising World: Some Aspects of Macroeconomy, Agriculture, and Poverty, New Delhi: Academic Foundation.
[24] Hess, M., 2016, “Modeling and Pricing Precipitation Derivatives under Weather Forecasts”, International Journal of Theoretical and Applied Finance, Vol. 19 (7), 1-29.
[25] Hoyer, S., 2013, Wind Derivatives: Hedging Wind Risk, Delft University of Technology, Netherlands.
[26] Huang, H.H., Shiu, Y.M., and Lin, P.S., 2008, “HDD and CDD Option Pricing with Market Price of Weather Risk for Taiwan”, Journal of Futures Markets, Vol. 28 (8), 790-814.
[27] Jeucken, M., 2004, Sustainable Finance and Banking: The Financial Sector and the Future of the Planet, London: Earthscan.
[28] Kimbarovsky, M., 2014, private correspondence, November 21. [Mike Kimbarovsky formerly traded OTC weather contracts for a merchant-energy trading firm, affiliated with their regulated entity.]
[29] Kremer, E., 1982, “A Characterization of the Esscher-transformation”, Astin Bulletin, Vol. 13, 57-59.
[30] Leobacher, G., Ngare, P., 2010, “On Modelling and Pricing Rainfall Derivatives with Seasonality”, Applied Mathematical Finance, Vol. 18 (1), 71-91.
[31] London, J., 2006, Modeling Derivatives Applications in Matlab, C++, and Excel, Jersey: Pearson Financial Times Press.
[32] Muller, A., Grandi, M., 2000, “Weather Derivatives: A Risk Management Tool for Weather-sensitive Industries”, The Geneva Papers on Risk and Insurance, Vol. 25, 273-287.
[33] Noven, R.C., Veraart, A.E.D., and Gandy, A., 2014, “A Lévy-driven Rainfall Model with Applications to Futures Pricing”, Advances in Statistical Analysis, Vol. 99 (4), 1-24.
[34] Odening, M., Musshoff, O., and Xu, W., 2007, “Analysis of Rainfall Derivatives Using Daily Precipitation Models: Opportunities and Pitfalls”, Agricultural Finance Review, Vol. 67, 135-156.
[35] Peng, Q. M., Chang, Z. R., and Chen, S. L., 2010, “Feasibility Study on Developing Weather Futures and Options in Taiwan”, Report to Taiwan Futures Exchange.
[36] Petzel, T., 2001, “Elusive Liquidity”, @Markets Magazine, January/February.
[37] Sands, R., Easton, G., 2011, “Crop Income Protection – Is It Worth It?”, Farmanco Facts, Vol. 32, 8-12.
[38] Shah, A., 2017, “Pricing of Rainfall Derivatives Using Generalized Linear Models of the Daily Rainfall Process”, International Agricultural Risk, Finance and Insurance Conference (IARFIC) 2017 Paris meetings paper.
[39] Skees, J. R., Black, J. R., and Barnett, B. J., 1997, “Designing and Rating an Area Yield Crop Insurance Contract”, American Journal of Agricultural Economics, Vol. 79, 430-438.
[40] Stowasser, M., 2012, “Modeling Rain Risk: A Multi-order Markov Chain Model Approach”, The Journal of Risk Finance, Vol. 13 (1), 45-60.
[41] Thind, S., 2014, “As Temperatures Tumble in North America, Weather Derivatives Warm Up,” Institutional Investor, January 23.
[42] Till, H., 2014, “Why Haven’t Weather Derivatives Been Mare Successful as Futures Contracts? A Case Study”, Journal of Governance and Regulation, Vol. 4, 367-371.
[43] Wilks, D.S., 2011, Statistical Methods in the Atmospheric Sciences, Vol. 100, Oxford: International Geophysics Series.
[44] Woolhiser, D.A., Pegram, G.G.S., 1979, “Maximum Likelihood Estimation of Fourier Coefficients to Describe Seasonal Variations of Parameters in Stochastic Daily Precipitation Models”, Journal of Applied Meteorology, Vol. 18, 34-42.
[45] Xu, W., Odening, M., and Musshoff, O., 2008, “Indifference Pricing of Weather Derivatives”, American Journal of Agricultural Economics, Vol. 90 (4), 979-993.
[46] Yoo, S. Y., 2004, Using Weather Derivatives to manage Financial Risk in Deregulated Electricity Markets. Ph.D., Cornell University, U.S.
[47] Zheng, J., Tao, S., 2017, “Stakeholder Analysis and Experience Reference of French Agricultural Mutual Insurance”, Journal of Inner Mongolia Agricultural University, Vol. 6, 23-29.
描述 碩士
國立政治大學
金融學系
106352048
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106352048
資料類型 thesis
dc.contributor.advisor 林士貴<br>莊明哲zh_TW
dc.contributor.advisor Lin, Shih-Kuei<br>Chuang, Ming-Cheen_US
dc.contributor.author (Authors) 方東杰zh_TW
dc.contributor.author (Authors) Fang, Dong-Jieen_US
dc.creator (作者) 方東杰zh_TW
dc.creator (作者) Fang, Dong-Jieen_US
dc.date (日期) 2019en_US
dc.date.accessioned 7-Aug-2019 16:13:44 (UTC+8)-
dc.date.available 7-Aug-2019 16:13:44 (UTC+8)-
dc.date.issued (上傳時間) 7-Aug-2019 16:13:44 (UTC+8)-
dc.identifier (Other Identifiers) G0106352048en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/124744-
dc.description (描述) 碩士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) 106352048zh_TW
dc.description.abstract (摘要) 本文討論了CME發行之雨量衍生性商品——雨量指數二元式合約之評價與風險管理。標的之雨量指數由兩種模型所刻畫：以一階兩狀態馬爾可夫鏈建立的發生模型，以及以混合指數分配建立的雨量強度模型。爲了捕捉降雨的季節性特徵，上述兩模型中的參數均以截斷傅立葉級數擬合，其中之係數以最大概似估計法估計，階數根據AIC與BIC判定。在以蒙地卡羅模擬獲得日降雨量模擬路徑後，計算月降雨量並以常態逆高斯分配擬合。鑒於天氣衍生性商品市場之不完備性，本文利用Esscher變換對雨量指數二元式選擇權進行評價，並以CME之真實市場價格校準獲得風險市場價格。最後，利用燃燒分析與敏感度分析討論雨量衍生性商品之風險管理。zh_TW
dc.description.abstract (摘要) In this paper we discuss the valuation and risk management of rainfall index binary contracts, which is a type of precipitation derivatives issued in CME. We describe the underlying rainfall index by occurrence model with first-order, two-state Markov chain, and magnitude model with mixed-exponential distribution. In order to capture the seasonality characteristics of precipitation, the parameters in both models are described with truncated Fourier series, in which the coefficients are fitted by MLE, and the orders are determined by AIC and BIC. We simulate the daily rainfall index by Monte Carlo simulation, and fit the simulated monthly rainfall index with NIG distribution. Since weather derivatives market is an incomplete market, we value the rainfall index binary options by using Esscher transform. The market price of risk is calibrated with real market data from CME. And the risk management of precipitation derivatives is discussed by using burn analysis and sensitivity analysis.en_US
dc.description.tableofcontents Contents
1 Introduction 1
2 Literatures Review 5
2.1 Weather Risk Market 5
2.1.1 Weather Insurances 5
2.1.2 Weather Derivatives 6
2.2 Pricing of Precipitation Derivatives 6
2.2.1 Models of Precipitation 7
2.2.2 Models of Pricing Precipitation Derivatives 8
3 The Weather Risk Market 10
3.1 Weather Risk 10
3.2 Weather Risk Management in Insurances 11
3.2.1 Agricultural Insurances in United States 11
3.2.2 Agricultural Insurances in France 13
3.2.3 Agricultural Insurances in Australia 14
3.2.4 Weather Index Insurances 15
3.3 Weather Risk Management in Derivatives 19
3.3.1 History of Market Development 19
3.3.2 Scale of Market 22
3.3.3 Market Participants 24
3.3.4 Weather Derivatives Contracts 25
4 The Models of Precipitation 30
4.1 Occurrence Model 31
4.2 Magnitude Model 32
4.3 Estimations 34
4.3.1 Maximum Likelihood Estimation 34
4.3.2 Order Determination of Fourier Series 37
5 The Model of Pricing Precipitation Derivatives 39
5.1 Simulation Method of Precipitation 39
5.1.1 Simulation of Occurrence Model 39
5.1.2 Simulation of Magnitude Model 40
5.2 Esscher Transform 41
5.3 Pricing Formulas 43
5.3.1 Rainfall Index Future 43
5.3.2 Rainfall Index Binary Option 44
6 Empirical Analysis 46
6.1 Data 46
6.1.1 Precipitation Derivatives Market Data 46
6.1.2 Precipitation Data 46
6.2 Estimations of Precipitation Models 48
6.2.1 Estimation of Occurrence Model 48
6.2.2 Estimation of Magnitude Model 50
6.3 Simulation and Estimation of Index Distribution 53
6.4 Theoretical Prices and Risk Management 54
6.4.1 Burn Analysis 54
6.4.2 Sensitivity Analysis 55
6.4.3 Market Price of Risk 56
7 Conclusion 59
Bibliography 61
Appendix A Results of Estimation 66
Appendix B Results of Simulation 69
Appendix C Results of Empirical Analysis 71
Appendix D Proof of Formula 77		zh_TW
dc.format.extent 3910471 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106352048en_US
dc.subject (關鍵詞) 雨量衍生性商品zh_TW
dc.subject (關鍵詞) 馬可夫鏈zh_TW
dc.subject (關鍵詞) 截斷傅立葉級數zh_TW
dc.subject (關鍵詞) Esscher變換zh_TW
dc.subject (關鍵詞) 風險市場價格zh_TW
dc.subject (關鍵詞) Precipitation derivativesen_US
dc.subject (關鍵詞) Markov Chainen_US
dc.subject (關鍵詞) Truncated fourier seriesen_US
dc.subject (關鍵詞) Esscher transformen_US
dc.subject (關鍵詞) Market price of risken_US
dc.title (題名) 天氣衍生性商品評價與風險管理：CME雨量指數二元式合約之應用zh_TW
dc.title (題名) Valuation and Risk Management of Weather Derivatives: the Application of CME Rainfall Index Binary Contractsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Aanderud, W. G., 1982, “Federal Crop Insurance”, Economics Commentator, Vol. 178, 1-3.
[2] Alexandridis, A. K., Zapranis, A. D., Weather Derivatives: Modeling and Pricing Weather-Related Risk, New York: Springer.
[3] Benth, F.E., Persio, L.D., and Lavagnini, S., 2018, “Stochastic Modeling of Wind Derivatives in Energy Markets”, Risks, Vol.6 (2), 1-21.
[4] Benth, F.E., Šaltytė-Benth, J., and Koekebakker, S., 2007, “Putting A Price on Temperature”, Scandinavian Journal of Statistics, Vol. 34, 746-767.
[5] Benth, F. E., Šaltytė-Benth, J., 2012, Modeling and Pricing in Financial Markets for Weather Derivatives, Singapore: World Scientific.
[6] Bowe, R., Hertzler, G., and Barnett, R. et al., 2003, “Final Report: Multi Peril Crop Insurance Task Force”, Report to the Minister for Agriculture, Forestry and Fisheries.
[7] Brockett, P.L., Wang, M., Yang, C., and Zou, H., 2006, “Portfolio Effects and Valuation of Weather Derivatives”, The Financial Review, Vol. 41 (1), 55-76.
[8] Bühlmann, H., 1980, “An Economic Premium Principle”, Astin Bulletin, Vol. 11, 52-60.
[9] Cabrera, B.L., Odening, M., and Ritter, M., 2013, “Pricing Rainfall Futures at the CME”, Journal of Banking & Finance, Vol.37, 4286-4298.
[10] Cao, M., Li, A., and Wei, J., 2004, “Precipitation Modeling and Contract Valuation: A Frontier in Weather Derivatives”, The Journal of Alternative Investments, Vol.7, 93-99.
[11] Carmona, R., Diko, P., 2004, “Pricing Precipitation Based Derivatives”, International Journal of Theoretical and Applied Finance, Vol. 8 (7), 959-988.
[12] Chen, Y., 2016, “Analysis and Enlightenment of Agricultural System in France, India and Japan”, World Agriculture, Vol. 7, 188-191.
[13] Chite, R. M., 2014, “The 2014 Farm Bill (P.L. 113-79): Summary and Side-by-Side”, Congressional Research Service: http://nationalaglawcenter.org/wp-content/uploads/assets/crs/R43076.pdf
[14] Cramer, S., Kampouridis, M., Freitas, A.A., and Alexandridis, A.K., 2017, “An extensive evaluation of seven machine learning methods for rainfall prediction in weather derivatives”, Expert Systems with Applications, Vol. 85, 169-181.
[15] Dischel, R. S., 1998, “The Fledgling Weather Market Takes Off”, Applied Derivatives Trading Focus, http://www.adtrading.com.
[16] Dorfleitner, G., Wimmer, M, 2010, “The Pricing of Temperature Futures at the Chicago Mercantile Exchange”, Journal of Banking & Finance, Vol. 34 (6), 1360-1370.
[17] Esscher, F., 1932, “On the Probability Function in the Collective Theory of Risk”, Scandinavian Actuarial Journal, Vol. 15, 175-195.
[18] Frittelli, M., 2000, “The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets”, Mathematical Finance, Vol. 10, 39-52.
[19] Halcrow, H. G., 1949, “Actuarial Structures for Crop Insurance”, Journal of Farm Economics, Vol. 31, 418-443.
[20] Härdle, W.K., Osipenko, M., 2017, “A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk”, International Journal of Financial Studies, Vol. 5(4), 1-18.
[21] Hatt, M., Heyhoe, E., and Whittle, L., 2012, “Options for Insuring Australian Agriculture”, ABARES report to client prepared for Climate Division, the Department of Agriculture, Fisheries and Forestry.
[22] Hazell, P., Anderson, J., Balzer, N., Clemmensen, A. H., Hess, U. and Rispoli, F., 2010, “The Potential for Scale and Sustainability in Weather Index Insurance for Agriculture and Rural Livelihoods”, International Fund for Agricultural Development and World Food Programme.
[23] Hazell, P., Skees, J. R., 2006, “Insuring against Bad Weather: Recent Thinking”, India in a Globalising World: Some Aspects of Macroeconomy, Agriculture, and Poverty, New Delhi: Academic Foundation.
[24] Hess, M., 2016, “Modeling and Pricing Precipitation Derivatives under Weather Forecasts”, International Journal of Theoretical and Applied Finance, Vol. 19 (7), 1-29.
[25] Hoyer, S., 2013, Wind Derivatives: Hedging Wind Risk, Delft University of Technology, Netherlands.
[26] Huang, H.H., Shiu, Y.M., and Lin, P.S., 2008, “HDD and CDD Option Pricing with Market Price of Weather Risk for Taiwan”, Journal of Futures Markets, Vol. 28 (8), 790-814.
[27] Jeucken, M., 2004, Sustainable Finance and Banking: The Financial Sector and the Future of the Planet, London: Earthscan.
[28] Kimbarovsky, M., 2014, private correspondence, November 21. [Mike Kimbarovsky formerly traded OTC weather contracts for a merchant-energy trading firm, affiliated with their regulated entity.]
[29] Kremer, E., 1982, “A Characterization of the Esscher-transformation”, Astin Bulletin, Vol. 13, 57-59.
[30] Leobacher, G., Ngare, P., 2010, “On Modelling and Pricing Rainfall Derivatives with Seasonality”, Applied Mathematical Finance, Vol. 18 (1), 71-91.
[31] London, J., 2006, Modeling Derivatives Applications in Matlab, C++, and Excel, Jersey: Pearson Financial Times Press.
[32] Muller, A., Grandi, M., 2000, “Weather Derivatives: A Risk Management Tool for Weather-sensitive Industries”, The Geneva Papers on Risk and Insurance, Vol. 25, 273-287.
[33] Noven, R.C., Veraart, A.E.D., and Gandy, A., 2014, “A Lévy-driven Rainfall Model with Applications to Futures Pricing”, Advances in Statistical Analysis, Vol. 99 (4), 1-24.
[34] Odening, M., Musshoff, O., and Xu, W., 2007, “Analysis of Rainfall Derivatives Using Daily Precipitation Models: Opportunities and Pitfalls”, Agricultural Finance Review, Vol. 67, 135-156.
[35] Peng, Q. M., Chang, Z. R., and Chen, S. L., 2010, “Feasibility Study on Developing Weather Futures and Options in Taiwan”, Report to Taiwan Futures Exchange.
[36] Petzel, T., 2001, “Elusive Liquidity”, @Markets Magazine, January/February.
[37] Sands, R., Easton, G., 2011, “Crop Income Protection – Is It Worth It?”, Farmanco Facts, Vol. 32, 8-12.
[38] Shah, A., 2017, “Pricing of Rainfall Derivatives Using Generalized Linear Models of the Daily Rainfall Process”, International Agricultural Risk, Finance and Insurance Conference (IARFIC) 2017 Paris meetings paper.
[39] Skees, J. R., Black, J. R., and Barnett, B. J., 1997, “Designing and Rating an Area Yield Crop Insurance Contract”, American Journal of Agricultural Economics, Vol. 79, 430-438.
[40] Stowasser, M., 2012, “Modeling Rain Risk: A Multi-order Markov Chain Model Approach”, The Journal of Risk Finance, Vol. 13 (1), 45-60.
[41] Thind, S., 2014, “As Temperatures Tumble in North America, Weather Derivatives Warm Up,” Institutional Investor, January 23.
[42] Till, H., 2014, “Why Haven’t Weather Derivatives Been Mare Successful as Futures Contracts? A Case Study”, Journal of Governance and Regulation, Vol. 4, 367-371.
[43] Wilks, D.S., 2011, Statistical Methods in the Atmospheric Sciences, Vol. 100, Oxford: International Geophysics Series.
[44] Woolhiser, D.A., Pegram, G.G.S., 1979, “Maximum Likelihood Estimation of Fourier Coefficients to Describe Seasonal Variations of Parameters in Stochastic Daily Precipitation Models”, Journal of Applied Meteorology, Vol. 18, 34-42.
[45] Xu, W., Odening, M., and Musshoff, O., 2008, “Indifference Pricing of Weather Derivatives”, American Journal of Agricultural Economics, Vol. 90 (4), 979-993.
[46] Yoo, S. Y., 2004, Using Weather Derivatives to manage Financial Risk in Deregulated Electricity Markets. Ph.D., Cornell University, U.S.
[47] Zheng, J., Tao, S., 2017, “Stakeholder Analysis and Experience Reference of French Agricultural Mutual Insurance”, Journal of Inner Mongolia Agricultural University, Vol. 6, 23-29.		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU201900165en_US