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題名 歐式能源期貨選擇權評價： 以WTI原油為例
Valuation of European Energy Futures Option： A Case Study of WTI Oil作者 鄧怡婷
Deng, I Ting貢獻者 林士貴
Lin, Shih Kuei
鄧怡婷
Deng, I Ting關鍵詞 期貨選擇權
均數回歸
跳躍擴散
季節性
futures option
mean reversion
jump diffusion
seasonality日期 2011 上傳時間 1-Apr-2014 11:14:33 (UTC+8) 摘要 近年來，能源商品的價格隨著國際政治情勢、國際金融環境以及景氣循環的影響產生劇烈波動，基於避險的需求，衍生性商品交易量也逐漸增加。然而，在評價能源衍生性商品的過程中，即期價格動態模型的選擇對於訂價與避險的結果有著顯著的影響，如何選擇一個適當的動態模型以評價能源商品便成為本文研究的目標。在指數與股價選擇權的評價模型中，大多以Black and Scholes (1973)提出的選擇權評價模型作為基礎，但Black-Scholes模型是否適用於評價能源市場的選擇權價格卻是有待商榷。Schwartz (1997)提出以均數回歸模型 (Mean Reversion Model)描述能源即期價格，發現比Black-Scholes模型中所假設的即期價格動態模型更能描述能源市場即期價格的波動。本研究也考慮能源市場遇到重大事件而造成即期價格產生劇烈波動的情況，因此在模型中加入跳躍項以捕捉價格跳躍的現象。另外，能源商品的需求與季節變化有高度相關性，因此本文亦考量即期價格的變動會受到季節性的變動影響，在模型中加入季節性函數，以補捉季節性的價格變化。基於前述模型考量，本研究在各種描述能源商品即期價格特性的動態模型之下，推導各個模型的期貨選擇權定價公式，進一步測試各模型在金融風暴與非金融風暴期間的訂價誤差與避險誤差，以提供投資人或避險需求者於原油期貨選擇權模型選用上之參考。
In recent years, the price of energy commodities has fluctuated with the international political situation and the international financial environment. For the sake of hedging demands, the trading volume of derivatives has been gradually increasing. In the process of valuation of energy derivatives, choices of the spot price dynamics model have a significant impact on pricing and hedging. Therefore, how to choose an appropriate dynamic model to evaluate the energy commodities has been main purpose of this study. Two main models are tested in this paper. One is the option pricing model supposed by Black and Scholes (1973), and another is the mean reversion model supposed by Schwartz (1997). This study also considered the volatility of the spot price in the energy market in case of major events, so the researcher adds the jump to explore the mean reversion model. In addition, the demand for energy commodities is highly correlated with seasonal variations. The vibration of spot price often affected by the seasonal variations is considered in the research. Therefore, the researchers also take the seasonal function into the research to capture the seasonal price changes. Based on considerations described above, the pricing formula for each model of futures option is evaluated in the research. The researcher further tests the pricing errors and hedging errors of each model during the financial crises and non-financial crises in order to provide the investors and hedging demanders with some suggestions about selecting oil futures option models.參考文獻 Amin, K. I., Ng, V. and Pirrong, S. C. (1995), ”Valuing energy derivatives,” Risk Publications and Enron Capital & Trade Resources, 57-70.Bakshi, G., Cao, C. and Che, Z. (2010), “Option pricing and hedging performance under stochastic volatility and stochastic interest rates,” Handbook of Quantitative Finance and Risk Management, ch.37.Benth, F. E., Ekeland, L., Hauge, R. and Nielsen, B. F. (2003), “A note on arbitrage-free pricing of forward contracts in energy markets,” Applied Mathematical Finance, 10(4), 325-336.Bjerksund, P., and Ekern, S. (1995), “Contingent claims evaluation of mean-reverting cash flows in shipping,” in L. Trigeorgis, (Ed.), Real Options in Capital Investment: Models, Strategies, and Applications, Preager.Black, F. and Scholes, M. (1973), “The pricing of options and corporate liabilities,” Journal of Political Economy, 81, 637-654.Brennan, M. J. and Schwartz, E. S. (1985), “Evaluating natural resource investments,” The Journal of Business , 58, 135-157.Carr, P. R, and Jarrow, R. A. (1995), “A discrete time synthesis of derivative security valuation using a term structure of futures prices,” The Netherlands: North-Holland Publishing Co., 225-249.Clewlow, L. and Strickland, C. (2000), “Energy derivatives: pricing and risk management,” Lacima Pupblications.Cortazar, G. and Schwartz. E. S. (1994), “The valuation of commodity-contingent claims,” Journal of Derivatives, 1, 27-39.Dritschel, M. and Protter, P. (1999), “Complete markets with discontinuous security price,” Finance and Stochastics, 3, 203-214.Hilliard, J. E., and Reis, J. A. (1999), “Jump processes in commodity futures prices and options pricing,” American Journal of Agricultural Economics, 81, 273-286.Jensen, B., (1999), “Option pricing in the jump-diffusion model with a random jump amplitude: A complete market approach,” Working paper.Koekebakker, S., and G. Lien, (2004), “Volatility and price jumps in agricultural futures prices-evidence from wheat options,” American Journal of Agricultural Economics, 86, 1018-1031. Kou, S. G. (2001), “A jump diffusion model for option pricing,” Working paper. Kou, S. G. (2008), “Jump-diffusion models for asset pricing in financial engineering,” Handbooks in Operations Research and Management Science, 15, ch.2.Mayer, K., Schmid, T. and Weber, F. (2011), “Modeling electricity spot prices- combining mean-reversion, spikes and stochastic volatility,” Working Paper.Merton, R. C. (1973), “Theory of rational option pricing,” Journal of Economics and Management Science, 4(1), 141-183.Merton, R. C. (1976), “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, 3, 125-144.Pilipovic, D. (1997), “Energy risk: valuating and managing energy derivatives,” McGraw-Hill.Reismann, H. (1992), “Movements of the term structure of commodity futures and pricing of commodity claims,” Working Paper.Rubinstein, M. (1985), “Nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE options classes from August 23, 1976 through August 31,1978.” Journal of Finance, 40, 455-480.Schwartz, E. S. (1997), “The Stochastic Behaviour of Commodity Prices: Implications for Pricing and Hedging”, Journal of Finance, 52, 923 - 973.Weron, R. (2006), "Modeling and forecasting electricity loads and prices: a statistical approach," Wiley Finance. 描述 碩士
國立政治大學
金融研究所
99352023
100資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099352023 資料類型 thesis dc.contributor.advisor 林士貴 zh_TW dc.contributor.advisor Lin, Shih Kuei en_US dc.contributor.author (Authors) 鄧怡婷 zh_TW dc.contributor.author (Authors) Deng, I Ting en_US dc.creator (作者) 鄧怡婷 zh_TW dc.creator (作者) Deng, I Ting en_US dc.date (日期) 2011 en_US dc.date.accessioned 1-Apr-2014 11:14:33 (UTC+8) - dc.date.available 1-Apr-2014 11:14:33 (UTC+8) - dc.date.issued (上傳時間) 1-Apr-2014 11:14:33 (UTC+8) - dc.identifier (Other Identifiers) G0099352023 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/65061 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融研究所 zh_TW dc.description (描述) 99352023 zh_TW dc.description (描述) 100 zh_TW dc.description.abstract (摘要) 近年來，能源商品的價格隨著國際政治情勢、國際金融環境以及景氣循環的影響產生劇烈波動，基於避險的需求，衍生性商品交易量也逐漸增加。然而，在評價能源衍生性商品的過程中，即期價格動態模型的選擇對於訂價與避險的結果有著顯著的影響，如何選擇一個適當的動態模型以評價能源商品便成為本文研究的目標。在指數與股價選擇權的評價模型中，大多以Black and Scholes (1973)提出的選擇權評價模型作為基礎，但Black-Scholes模型是否適用於評價能源市場的選擇權價格卻是有待商榷。Schwartz (1997)提出以均數回歸模型 (Mean Reversion Model)描述能源即期價格，發現比Black-Scholes模型中所假設的即期價格動態模型更能描述能源市場即期價格的波動。本研究也考慮能源市場遇到重大事件而造成即期價格產生劇烈波動的情況，因此在模型中加入跳躍項以捕捉價格跳躍的現象。另外，能源商品的需求與季節變化有高度相關性，因此本文亦考量即期價格的變動會受到季節性的變動影響，在模型中加入季節性函數，以補捉季節性的價格變化。基於前述模型考量，本研究在各種描述能源商品即期價格特性的動態模型之下，推導各個模型的期貨選擇權定價公式，進一步測試各模型在金融風暴與非金融風暴期間的訂價誤差與避險誤差，以提供投資人或避險需求者於原油期貨選擇權模型選用上之參考。 zh_TW dc.description.abstract (摘要) In recent years, the price of energy commodities has fluctuated with the international political situation and the international financial environment. For the sake of hedging demands, the trading volume of derivatives has been gradually increasing. In the process of valuation of energy derivatives, choices of the spot price dynamics model have a significant impact on pricing and hedging. Therefore, how to choose an appropriate dynamic model to evaluate the energy commodities has been main purpose of this study. Two main models are tested in this paper. One is the option pricing model supposed by Black and Scholes (1973), and another is the mean reversion model supposed by Schwartz (1997). This study also considered the volatility of the spot price in the energy market in case of major events, so the researcher adds the jump to explore the mean reversion model. In addition, the demand for energy commodities is highly correlated with seasonal variations. The vibration of spot price often affected by the seasonal variations is considered in the research. Therefore, the researchers also take the seasonal function into the research to capture the seasonal price changes. Based on considerations described above, the pricing formula for each model of futures option is evaluated in the research. The researcher further tests the pricing errors and hedging errors of each model during the financial crises and non-financial crises in order to provide the investors and hedging demanders with some suggestions about selecting oil futures option models. en_US dc.description.tableofcontents 1. 緒論 1 1.1 研究背景與動機 1 1.2 研究目的 2 1.3 論文架構 22. 文獻探討 4 2.1 能源期貨與能源期貨選擇權 4 2.2 模型假設 5 2.2.1 Black-Scholes模型 6 2.2.2均數回歸模型 6 2.2.3均數回歸與跳躍擴散模型 7 2.2.4均數回歸與季節性 83. 模型與假設 9 3.1 Black-Scholes模型 9 3.2 均數回歸模型 10 3.3均數回歸與跳躍擴散模型 12 3.4 均數回歸與季節性模型 13 3.5均數回歸季節性與跳躍模型 15 3.6 模型假設 164. 歐式期貨選擇權評價公式與避險 18 4.1 Black-Scholes 歐式期貨選擇權評價公式與避險 18 4.2均數回歸模型下歐式期貨選擇權評價公式與避險 20 4.3均數回歸與跳躍模型下歐式期貨選擇權評價公式與避險 21 4.4均數回歸季節性模型下歐式期貨選擇權評價公式與避險 23 4.5均數回歸季節性與跳躍模型下歐式期貨選擇權評價公式與避險 245. 實證分析 27 5.1 資料描述與研究樣本 27 5.2 資料分析與參數估計 27 5.2.1 敘述統計 27 5.2.2 參數估計 28 5.3 期貨選擇權訂價誤差 30 5.4 投資組合避險價格誤差 336. 結論 35參考文獻 36附錄 38附錄A. Black-Scholes歐式期貨選擇權評價公式 38附錄B. 均數回歸模型下期貨評價公式 39附錄C. 均數回歸與跳躍擴散模型期貨評價公式 41附錄D. 均數回歸與季節性模型下期貨評價公式 45附錄E. 均數回歸季節性與跳躍擴散模型下期貨評價公式 48附錄F. 跳躍模型下即期價格轉期貨價格部分解 51附錄G. 避險參數(Delta) 53 zh_TW dc.format.extent 2711240 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099352023 en_US dc.subject (關鍵詞) 期貨選擇權 zh_TW dc.subject (關鍵詞) 均數回歸 zh_TW dc.subject (關鍵詞) 跳躍擴散 zh_TW dc.subject (關鍵詞) 季節性 zh_TW dc.subject (關鍵詞) futures option en_US dc.subject (關鍵詞) mean reversion en_US dc.subject (關鍵詞) jump diffusion en_US dc.subject (關鍵詞) seasonality en_US dc.title (題名) 歐式能源期貨選擇權評價： 以WTI原油為例 zh_TW dc.title (題名) Valuation of European Energy Futures Option： A Case Study of WTI Oil en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Amin, K. I., Ng, V. and Pirrong, S. C. (1995), ”Valuing energy derivatives,” Risk Publications and Enron Capital & Trade Resources, 57-70.Bakshi, G., Cao, C. and Che, Z. (2010), “Option pricing and hedging performance under stochastic volatility and stochastic interest rates,” Handbook of Quantitative Finance and Risk Management, ch.37.Benth, F. E., Ekeland, L., Hauge, R. and Nielsen, B. F. (2003), “A note on arbitrage-free pricing of forward contracts in energy markets,” Applied Mathematical Finance, 10(4), 325-336.Bjerksund, P., and Ekern, S. (1995), “Contingent claims evaluation of mean-reverting cash flows in shipping,” in L. Trigeorgis, (Ed.), Real Options in Capital Investment: Models, Strategies, and Applications, Preager.Black, F. and Scholes, M. (1973), “The pricing of options and corporate liabilities,” Journal of Political Economy, 81, 637-654.Brennan, M. J. and Schwartz, E. S. (1985), “Evaluating natural resource investments,” The Journal of Business , 58, 135-157.Carr, P. R, and Jarrow, R. A. (1995), “A discrete time synthesis of derivative security valuation using a term structure of futures prices,” The Netherlands: North-Holland Publishing Co., 225-249.Clewlow, L. and Strickland, C. (2000), “Energy derivatives: pricing and risk management,” Lacima Pupblications.Cortazar, G. and Schwartz. E. S. (1994), “The valuation of commodity-contingent claims,” Journal of Derivatives, 1, 27-39.Dritschel, M. and Protter, P. (1999), “Complete markets with discontinuous security price,” Finance and Stochastics, 3, 203-214.Hilliard, J. E., and Reis, J. A. (1999), “Jump processes in commodity futures prices and options pricing,” American Journal of Agricultural Economics, 81, 273-286.Jensen, B., (1999), “Option pricing in the jump-diffusion model with a random jump amplitude: A complete market approach,” Working paper.Koekebakker, S., and G. Lien, (2004), “Volatility and price jumps in agricultural futures prices-evidence from wheat options,” American Journal of Agricultural Economics, 86, 1018-1031. Kou, S. G. (2001), “A jump diffusion model for option pricing,” Working paper. Kou, S. G. (2008), “Jump-diffusion models for asset pricing in financial engineering,” Handbooks in Operations Research and Management Science, 15, ch.2.Mayer, K., Schmid, T. and Weber, F. (2011), “Modeling electricity spot prices- combining mean-reversion, spikes and stochastic volatility,” Working Paper.Merton, R. C. (1973), “Theory of rational option pricing,” Journal of Economics and Management Science, 4(1), 141-183.Merton, R. C. (1976), “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, 3, 125-144.Pilipovic, D. (1997), “Energy risk: valuating and managing energy derivatives,” McGraw-Hill.Reismann, H. (1992), “Movements of the term structure of commodity futures and pricing of commodity claims,” Working Paper.Rubinstein, M. (1985), “Nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE options classes from August 23, 1976 through August 31,1978.” Journal of Finance, 40, 455-480.Schwartz, E. S. (1997), “The Stochastic Behaviour of Commodity Prices: Implications for Pricing and Hedging”, Journal of Finance, 52, 923 - 973.Weron, R. (2006), "Modeling and forecasting electricity loads and prices: a statistical approach," Wiley Finance. zh_TW
