學術產出-Theses

Article View/Open

Publication Export

Google ScholarTM

政大圖書館

Citation Infomation

  • No doi shows Citation Infomation
題名 混合結構型商品個案分析
Hybrid structure product case analysis
作者 游宗憲
Yu, Tsung Hsien
貢獻者 陳松男
Chen, Son Nan
游宗憲
Yu, Tsung Hsien
關鍵詞 混合結構性商品
Extended BGM模型
WTI
遠期曲線模型
雪球型利率結構商品
Hybrid structure product
Extended BGM model
WTI
Forward curve model
Snowball
日期 2010
上傳時間 14-Oct-2011 13:40:57 (UTC+8)
摘要 2008年初,正值美國籠罩次級房貸風暴影響、全球經濟景氣趨緩、產油國地緣政治因素造成能源價格創新高…等險峻經濟狀況之際,投資銀行設計一包含 :搭配出局條款之CMS Spread雪球型利率結構商品及結合附加WTI上限、USD/JPY匯率上下限之異型選擇權的混合結構性商品提案。本文依據標的資產屬性,參考相關文獻及近期在頂級期刊發表之利率資產評價模型研究中,選用Extended BGM模型(Ting-Pin Wu, and Son-Nan Chen(2007))、遠期曲線模型及匯率評價模型為個案之基礎評價模型;以無套利觀念依取得之市場各資產相關公開報價資料估算各模型所需之參數;由於屬於雪球利率結構型商品及路徑相關特性,在目前相關文獻無封閉解的條件下,使用蒙地卡羅模擬獲得未來各資產之現金流折現值,進而計算預期理論價值。依據上述方法論評價所獲得之預期理論價格顯示,個案並非具公平價值之交易,依此結論強烈建議客戶不應該承做本交易。
      個案相當於投資銀行以買入一個5年期附帶出局條件,隱含看空經濟景氣循環之CMS Spread選擇權及買入一個1年期看空WTI價格選擇權建構此混合結構性商品。為強化客戶承做意願,設立一似乎觸及機會很大,但從交易後至今從未觸及的出局條件,又透過每日數位選擇權計息方式將WTI波動度資產化,提供大於10%之相對LIBOR rate 很高,但實際是被低估之半年收息固定費率。由於雪球型利率結構型商品特性,收益不僅取決於是否達成交易付款條件,更重要因素是達成時間點之速度。
      在蒙地卡羅模擬資產價格路徑中,觸及頭一次CMS Spread付款條件天數之眾數區間為125至135,貼近實際136天。從評價結果,交易之付款條件內已隱含透過兩個不同標的資產選擇權之高預期獲利相互達到避險、套利及強化收益等效益;投資銀行可以不用額外對受眾多複雜不確定因數影響之WTI價格採取避險策略,而將所有避險成本轉嫁於選擇權賣方的客戶。在資本計提規範下及確保未來預期收益之考量下,投資銀行唯一要做是以低成本尋求中介銀行進行背對背交易以強化因市場風險所衍生之信用風險。
      從研究過程,不禁讚嘆個案是投資銀行設計建構在財務工程科學上的卓越藝術及策略,從它一旦出現世界上之瞬間,個人預估其價值將達34,211,458.09美元!
Early 2008 was a steep economic era when U.S. was enveloped by subprimemortgage crisis, world`s economy was slowing down, and energy prices were pushed to a historical record high by oil geopolitical factors. Under this situation, an investmentbank designed a hybrid structure product, which includes a CMS Spread Snowball interest rate structured product with USD/JPY FX rate Knock out condition, a WTIoption of an additional upper limit, a USD/JPY exchange rate combined exotic option of upper and lower limits. After considering assets attributes and reviewing the relevant literature and recent research published in top journals related to the interest rate assetpricing model, Extended BGM model (Ting-Pin Wu, and Son-Nan Chen (2007)), forward curve model, and FX Rate model are selected as the basic pricing models. Tocalculate the expected theoretical value of this structured product, the unavailable model parameters of assets are estimated through the public market data based on thearbitrage-free concept, and the discounted values of the assets future cash flows are obtained by Monte Carlo simulation because of snowball interest rate structured product and path dependency characteristic and no close form solution in current relevant literature. The results of the pricing models shows that the net present value(NPV) received by customers is lower than that received by the investment bank, theconclusion is : Strongly recommend customers should not to do this trade !
      In this case, the investment bank used a long position of one 5-year period CMSSpread Option with knock out condition, which implies Bearish on the economic cycle, and a short position of a 1-year period WTI option with up and low limits condition to construct this hybrid structure product. To draw customers’ attention to this proposal, the investment bank designed a knock out condition that seemed to be met very easily,but the price never touched by the article finished date. Additionally, a daily accrued
     digital option is used to transfer WTI volatility to a semi-annual fixed yield over 10% that, compared to LIBOR Rate, is very high but actually is underestimated. For theSnowball structure product, the total profit depends on not only when but also, more importantly, how soon to meet the payment condition.
      According to the asset pricing path generated by Monte Carlo simulation, the mode range which CMS Spread payment condition first met is 125 to 135 days after the contract’s value date, very close to the actually history data of 136 days. From pricing results, terms of contract implied that two different options combined to hedge risk and gain profit from each other. Hence, the investment bank does not need to make extrahedge strategy to WTI price which is impacted by more complicated risk factors.However, customer must spend hedge cost because of taking much risk as a sell option role. Under the Capital Charge regulation, to lock up the expected profit, what the investment bank needs to do is only to pay a very low cost fee, which like insurancepremium, to look for an intermediary bank to offer a back to back trade to manage thecredit risk caused by market risk!
      During the research of this paper, I am amazed what an excellent art and strategy that designed by the investment bank based on financial engineering science! As this structure product appeared in this world, I estimated that it would worth 34,211,458.09 USD.
第一章 緒論 1
     第一節 研究動機與目的 1
     第二節 研究架構與研究流程 3
     第二章 文獻回顧 5
     第一節 能源價格模型相關文獻 5
     第二節 利率模型相關文獻 8
     第三章 研究方法 13
     第一節 研究設計概述 13
     第二節 利率、能源、匯率各類資產評價模型介紹 14
     第三節 蒙地卡羅(Monte Carlo)模擬及機率測度選擇 20
     第四節 市場資料收集及轉換研究方法介紹 21
     第五節 參數校正 24
     第六節 主成份分析及資料維度縮減方法介紹 26
     第四章 個案說明及收益分析 29
     第一節 Hybrid structure product介紹 29
     第二節 經濟資料介紹與分析 30
     第三節 個案交易契約介紹及分析 36
     第四節 個案交易之收益分析 39
     第五章 個案評價分析 42
     第一節 市場資料搜集及校準 42
     第二節 評價與避險參數分析 52
     第三節 模型與歷史市場資料差異分析 56
     第四節 投資銀行產品設計理念分析 60
     第六章 結論與建議 62
     參考文獻 63
     附錄 66
參考文獻 1. 李明翰(2005),「殖利率曲線負斜率」大華證券報告。
2. 李婉瑜(2001),「金融風暴前後亞洲各國股匯市波動性之相關研究」,東吳大學經濟學系碩士班碩士論文。
3. 林清山,多變項分析統計法,東華書局,1990年。
4. 陳松男(2006),利率金融工程學:理論模型與實務應用,新陸書局。
5. 陳松男(2005A),金融工程學:金融商品創新選擇權理論(二版) ,新陸書局。
6. 陳松男(2004),結構型金融商品之設計及創新 ,新陸書局。
7. 陳松男(2005B),結構型金融商品之設計及創新(二) ,新陸書局。
8. 陳松男(1996),「選擇權與期貨」,新陸書局。
9. 國際經濟金融情勢(民國96年第3季),中央銀行季刊, 第29 卷, 第4期, 民國97 年, 第115 - 138 頁。
10. 傅粹馨,主成份分析和共同因素分析相關議題之探究,教育與社會研究,第三期(2002/2),pp107-132。
11. 楊蓁海,「我國銀行存放款利差減少原因剖析與因應對策」 中央銀行季刊, 第29 卷, 第2期, 民國96 年, 第45 - 82 頁。
12. Back, K (2005), “A Course in Derivative Securities: Introduction to Theory and Computation, ”Springer Finance.
13. Black, F., (1976), “The Pricing of Commodity Contracts,” Journal of Financial Economics ,Vol. 3, pp. 167–179.
14. Black, F., Derman, E., Toy, W., (1990), “A One-Factor Model of Interest Rates and Its Application to Treasury bond options,” Financial Analysts Journal, pp. 33-39.
15. Brace, A., Gatarek, D., Musiela, M., (1997), “The market model of interest rate dynamics,” Mathematical Finance, Vol. 7, pp. 127–147.
16. Brennan, M.J., Schwartz, E.S., (1980), “Analyzing Convertible Bonds,” Journal of Financial and Quantitative Analysis, Vol. 15, pp. 907-929.
17. Brigo, D., and Mercurio, F (2006), “Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, ” Springer Finance.
18. Cairns, A.J.G., (2004), “Interest rate models, ”Princeton University Press, Princeton.
19. Dothan, U.L., (1978), “On the Term Structure of Interest Rates,” Journal of Financial Economics, Vol. 6 pp. 59-69.
20. Heath, D., Jarrow, R., Morton, A., (1992), “Bond Pricing and The Term Structure of Interest rates: A New Methodology for Contingent Claims Valuation,” Economeyrica, Vol. 60, pp. 77–105.
21. Ho, T.S.Y., Lee, S.B.,(1986), “Term Structure Movements and Pricing Interest Rates Contingent Claims,” Journal of Finance, Vol. 41, pp. 1011–1029.
22. Hull, J., White, A., (1990), “Pricing Interest-Rate-Derivative Securities,” Review of Financial Studies, Vol. 3(4), pp. 573–592.
23. Hull, J., White, A.,(1994b), “Numerical Procedures for Implementing Term Structure Models I: Single-factor models,” Journal of Derivatives, pp. 7–16.
24. Jamshidian, F., (1997), “LIBOR and Swap Market Models and Measures,” Finance and Stochastics, Vol. 1, pp. 293–330.
25. Les Clewlow and Chris Strickland (2000), “Energy Derivatives: Pricing and Risk Management , ” Lacima Publications.
26. Piterbarg. V. V., (2004b), “Pricing and Hedging Callable Libor Exotics in Forward Libor Models,” Journal of Computational Finance, Vol. 8(2), pp. 65-117.
27. Rebonato, R. (2002), “Modern Pricing of Interest-Rate Derivatives: The LIBOR Market Model and Beyond, ” Princeton University Press.
28. Schwartz, E., “The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging,” The Journal of Finance, Vol. 52(3), pp. 923-973, 1997.
29. Ting-Pin Wu, and Son-Nan Chen(2007),”Cross-Currency Equity Swaps in the BGM Model,” The Journal of Derivatives, Winter 2007,pp61-76
30. Vasicek, O., (1977), “An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics, Vol. 5, pp. 177-88.
描述 碩士
國立政治大學
經營管理碩士學程(EMBA)
97932203
99
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097932203
資料類型 thesis
dc.contributor.advisor 陳松男zh_TW
dc.contributor.advisor Chen, Son Nanen_US
dc.contributor.author (Authors) 游宗憲zh_TW
dc.contributor.author (Authors) Yu, Tsung Hsienen_US
dc.creator (作者) 游宗憲zh_TW
dc.creator (作者) Yu, Tsung Hsienen_US
dc.date (日期) 2010en_US
dc.date.accessioned 14-Oct-2011 13:40:57 (UTC+8)-
dc.date.available 14-Oct-2011 13:40:57 (UTC+8)-
dc.date.issued (上傳時間) 14-Oct-2011 13:40:57 (UTC+8)-
dc.identifier (Other Identifiers) G0097932203en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/51678-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 經營管理碩士學程(EMBA)zh_TW
dc.description (描述) 97932203zh_TW
dc.description (描述) 99zh_TW
dc.description.abstract (摘要) 2008年初,正值美國籠罩次級房貸風暴影響、全球經濟景氣趨緩、產油國地緣政治因素造成能源價格創新高…等險峻經濟狀況之際,投資銀行設計一包含 :搭配出局條款之CMS Spread雪球型利率結構商品及結合附加WTI上限、USD/JPY匯率上下限之異型選擇權的混合結構性商品提案。本文依據標的資產屬性,參考相關文獻及近期在頂級期刊發表之利率資產評價模型研究中,選用Extended BGM模型(Ting-Pin Wu, and Son-Nan Chen(2007))、遠期曲線模型及匯率評價模型為個案之基礎評價模型;以無套利觀念依取得之市場各資產相關公開報價資料估算各模型所需之參數;由於屬於雪球利率結構型商品及路徑相關特性,在目前相關文獻無封閉解的條件下,使用蒙地卡羅模擬獲得未來各資產之現金流折現值,進而計算預期理論價值。依據上述方法論評價所獲得之預期理論價格顯示,個案並非具公平價值之交易,依此結論強烈建議客戶不應該承做本交易。
      個案相當於投資銀行以買入一個5年期附帶出局條件,隱含看空經濟景氣循環之CMS Spread選擇權及買入一個1年期看空WTI價格選擇權建構此混合結構性商品。為強化客戶承做意願,設立一似乎觸及機會很大,但從交易後至今從未觸及的出局條件,又透過每日數位選擇權計息方式將WTI波動度資產化,提供大於10%之相對LIBOR rate 很高,但實際是被低估之半年收息固定費率。由於雪球型利率結構型商品特性,收益不僅取決於是否達成交易付款條件,更重要因素是達成時間點之速度。
      在蒙地卡羅模擬資產價格路徑中,觸及頭一次CMS Spread付款條件天數之眾數區間為125至135,貼近實際136天。從評價結果,交易之付款條件內已隱含透過兩個不同標的資產選擇權之高預期獲利相互達到避險、套利及強化收益等效益;投資銀行可以不用額外對受眾多複雜不確定因數影響之WTI價格採取避險策略,而將所有避險成本轉嫁於選擇權賣方的客戶。在資本計提規範下及確保未來預期收益之考量下,投資銀行唯一要做是以低成本尋求中介銀行進行背對背交易以強化因市場風險所衍生之信用風險。
      從研究過程,不禁讚嘆個案是投資銀行設計建構在財務工程科學上的卓越藝術及策略,從它一旦出現世界上之瞬間,個人預估其價值將達34,211,458.09美元!
zh_TW
dc.description.abstract (摘要) Early 2008 was a steep economic era when U.S. was enveloped by subprimemortgage crisis, world`s economy was slowing down, and energy prices were pushed to a historical record high by oil geopolitical factors. Under this situation, an investmentbank designed a hybrid structure product, which includes a CMS Spread Snowball interest rate structured product with USD/JPY FX rate Knock out condition, a WTIoption of an additional upper limit, a USD/JPY exchange rate combined exotic option of upper and lower limits. After considering assets attributes and reviewing the relevant literature and recent research published in top journals related to the interest rate assetpricing model, Extended BGM model (Ting-Pin Wu, and Son-Nan Chen (2007)), forward curve model, and FX Rate model are selected as the basic pricing models. Tocalculate the expected theoretical value of this structured product, the unavailable model parameters of assets are estimated through the public market data based on thearbitrage-free concept, and the discounted values of the assets future cash flows are obtained by Monte Carlo simulation because of snowball interest rate structured product and path dependency characteristic and no close form solution in current relevant literature. The results of the pricing models shows that the net present value(NPV) received by customers is lower than that received by the investment bank, theconclusion is : Strongly recommend customers should not to do this trade !
      In this case, the investment bank used a long position of one 5-year period CMSSpread Option with knock out condition, which implies Bearish on the economic cycle, and a short position of a 1-year period WTI option with up and low limits condition to construct this hybrid structure product. To draw customers’ attention to this proposal, the investment bank designed a knock out condition that seemed to be met very easily,but the price never touched by the article finished date. Additionally, a daily accrued
     digital option is used to transfer WTI volatility to a semi-annual fixed yield over 10% that, compared to LIBOR Rate, is very high but actually is underestimated. For theSnowball structure product, the total profit depends on not only when but also, more importantly, how soon to meet the payment condition.
      According to the asset pricing path generated by Monte Carlo simulation, the mode range which CMS Spread payment condition first met is 125 to 135 days after the contract’s value date, very close to the actually history data of 136 days. From pricing results, terms of contract implied that two different options combined to hedge risk and gain profit from each other. Hence, the investment bank does not need to make extrahedge strategy to WTI price which is impacted by more complicated risk factors.However, customer must spend hedge cost because of taking much risk as a sell option role. Under the Capital Charge regulation, to lock up the expected profit, what the investment bank needs to do is only to pay a very low cost fee, which like insurancepremium, to look for an intermediary bank to offer a back to back trade to manage thecredit risk caused by market risk!
      During the research of this paper, I am amazed what an excellent art and strategy that designed by the investment bank based on financial engineering science! As this structure product appeared in this world, I estimated that it would worth 34,211,458.09 USD.
en_US
dc.description.abstract (摘要) 第一章 緒論 1
     第一節 研究動機與目的 1
     第二節 研究架構與研究流程 3
     第二章 文獻回顧 5
     第一節 能源價格模型相關文獻 5
     第二節 利率模型相關文獻 8
     第三章 研究方法 13
     第一節 研究設計概述 13
     第二節 利率、能源、匯率各類資產評價模型介紹 14
     第三節 蒙地卡羅(Monte Carlo)模擬及機率測度選擇 20
     第四節 市場資料收集及轉換研究方法介紹 21
     第五節 參數校正 24
     第六節 主成份分析及資料維度縮減方法介紹 26
     第四章 個案說明及收益分析 29
     第一節 Hybrid structure product介紹 29
     第二節 經濟資料介紹與分析 30
     第三節 個案交易契約介紹及分析 36
     第四節 個案交易之收益分析 39
     第五章 個案評價分析 42
     第一節 市場資料搜集及校準 42
     第二節 評價與避險參數分析 52
     第三節 模型與歷史市場資料差異分析 56
     第四節 投資銀行產品設計理念分析 60
     第六章 結論與建議 62
     參考文獻 63
     附錄 66
-
dc.description.tableofcontents 第一章 緒論 1
     第一節 研究動機與目的 1
     第二節 研究架構與研究流程 3
     第二章 文獻回顧 5
     第一節 能源價格模型相關文獻 5
     第二節 利率模型相關文獻 8
     第三章 研究方法 13
     第一節 研究設計概述 13
     第二節 利率、能源、匯率各類資產評價模型介紹 14
     第三節 蒙地卡羅(Monte Carlo)模擬及機率測度選擇 20
     第四節 市場資料收集及轉換研究方法介紹 21
     第五節 參數校正 24
     第六節 主成份分析及資料維度縮減方法介紹 26
     第四章 個案說明及收益分析 29
     第一節 Hybrid structure product介紹 29
     第二節 經濟資料介紹與分析 30
     第三節 個案交易契約介紹及分析 36
     第四節 個案交易之收益分析 39
     第五章 個案評價分析 42
     第一節 市場資料搜集及校準 42
     第二節 評價與避險參數分析 52
     第三節 模型與歷史市場資料差異分析 56
     第四節 投資銀行產品設計理念分析 60
     第六章 結論與建議 62
     參考文獻 63
     附錄 66
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097932203en_US
dc.subject (關鍵詞) 混合結構性商品zh_TW
dc.subject (關鍵詞) Extended BGM模型zh_TW
dc.subject (關鍵詞) WTIzh_TW
dc.subject (關鍵詞) 遠期曲線模型zh_TW
dc.subject (關鍵詞) 雪球型利率結構商品zh_TW
dc.subject (關鍵詞) Hybrid structure producten_US
dc.subject (關鍵詞) Extended BGM modelen_US
dc.subject (關鍵詞) WTIen_US
dc.subject (關鍵詞) Forward curve modelen_US
dc.subject (關鍵詞) Snowballen_US
dc.title (題名) 混合結構型商品個案分析zh_TW
dc.title (題名) Hybrid structure product case analysisen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. 李明翰(2005),「殖利率曲線負斜率」大華證券報告。zh_TW
dc.relation.reference (參考文獻) 2. 李婉瑜(2001),「金融風暴前後亞洲各國股匯市波動性之相關研究」,東吳大學經濟學系碩士班碩士論文。zh_TW
dc.relation.reference (參考文獻) 3. 林清山,多變項分析統計法,東華書局,1990年。zh_TW
dc.relation.reference (參考文獻) 4. 陳松男(2006),利率金融工程學:理論模型與實務應用,新陸書局。zh_TW
dc.relation.reference (參考文獻) 5. 陳松男(2005A),金融工程學:金融商品創新選擇權理論(二版) ,新陸書局。zh_TW
dc.relation.reference (參考文獻) 6. 陳松男(2004),結構型金融商品之設計及創新 ,新陸書局。zh_TW
dc.relation.reference (參考文獻) 7. 陳松男(2005B),結構型金融商品之設計及創新(二) ,新陸書局。zh_TW
dc.relation.reference (參考文獻) 8. 陳松男(1996),「選擇權與期貨」,新陸書局。zh_TW
dc.relation.reference (參考文獻) 9. 國際經濟金融情勢(民國96年第3季),中央銀行季刊, 第29 卷, 第4期, 民國97 年, 第115 - 138 頁。zh_TW
dc.relation.reference (參考文獻) 10. 傅粹馨,主成份分析和共同因素分析相關議題之探究,教育與社會研究,第三期(2002/2),pp107-132。zh_TW
dc.relation.reference (參考文獻) 11. 楊蓁海,「我國銀行存放款利差減少原因剖析與因應對策」 中央銀行季刊, 第29 卷, 第2期, 民國96 年, 第45 - 82 頁。zh_TW
dc.relation.reference (參考文獻) 12. Back, K (2005), “A Course in Derivative Securities: Introduction to Theory and Computation, ”Springer Finance.zh_TW
dc.relation.reference (參考文獻) 13. Black, F., (1976), “The Pricing of Commodity Contracts,” Journal of Financial Economics ,Vol. 3, pp. 167–179.zh_TW
dc.relation.reference (參考文獻) 14. Black, F., Derman, E., Toy, W., (1990), “A One-Factor Model of Interest Rates and Its Application to Treasury bond options,” Financial Analysts Journal, pp. 33-39.zh_TW
dc.relation.reference (參考文獻) 15. Brace, A., Gatarek, D., Musiela, M., (1997), “The market model of interest rate dynamics,” Mathematical Finance, Vol. 7, pp. 127–147.zh_TW
dc.relation.reference (參考文獻) 16. Brennan, M.J., Schwartz, E.S., (1980), “Analyzing Convertible Bonds,” Journal of Financial and Quantitative Analysis, Vol. 15, pp. 907-929.zh_TW
dc.relation.reference (參考文獻) 17. Brigo, D., and Mercurio, F (2006), “Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, ” Springer Finance.zh_TW
dc.relation.reference (參考文獻) 18. Cairns, A.J.G., (2004), “Interest rate models, ”Princeton University Press, Princeton.zh_TW
dc.relation.reference (參考文獻) 19. Dothan, U.L., (1978), “On the Term Structure of Interest Rates,” Journal of Financial Economics, Vol. 6 pp. 59-69.zh_TW
dc.relation.reference (參考文獻) 20. Heath, D., Jarrow, R., Morton, A., (1992), “Bond Pricing and The Term Structure of Interest rates: A New Methodology for Contingent Claims Valuation,” Economeyrica, Vol. 60, pp. 77–105.zh_TW
dc.relation.reference (參考文獻) 21. Ho, T.S.Y., Lee, S.B.,(1986), “Term Structure Movements and Pricing Interest Rates Contingent Claims,” Journal of Finance, Vol. 41, pp. 1011–1029.zh_TW
dc.relation.reference (參考文獻) 22. Hull, J., White, A., (1990), “Pricing Interest-Rate-Derivative Securities,” Review of Financial Studies, Vol. 3(4), pp. 573–592.zh_TW
dc.relation.reference (參考文獻) 23. Hull, J., White, A.,(1994b), “Numerical Procedures for Implementing Term Structure Models I: Single-factor models,” Journal of Derivatives, pp. 7–16.zh_TW
dc.relation.reference (參考文獻) 24. Jamshidian, F., (1997), “LIBOR and Swap Market Models and Measures,” Finance and Stochastics, Vol. 1, pp. 293–330.zh_TW
dc.relation.reference (參考文獻) 25. Les Clewlow and Chris Strickland (2000), “Energy Derivatives: Pricing and Risk Management , ” Lacima Publications.zh_TW
dc.relation.reference (參考文獻) 26. Piterbarg. V. V., (2004b), “Pricing and Hedging Callable Libor Exotics in Forward Libor Models,” Journal of Computational Finance, Vol. 8(2), pp. 65-117.zh_TW
dc.relation.reference (參考文獻) 27. Rebonato, R. (2002), “Modern Pricing of Interest-Rate Derivatives: The LIBOR Market Model and Beyond, ” Princeton University Press.zh_TW
dc.relation.reference (參考文獻) 28. Schwartz, E., “The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging,” The Journal of Finance, Vol. 52(3), pp. 923-973, 1997.zh_TW
dc.relation.reference (參考文獻) 29. Ting-Pin Wu, and Son-Nan Chen(2007),”Cross-Currency Equity Swaps in the BGM Model,” The Journal of Derivatives, Winter 2007,pp61-76zh_TW
dc.relation.reference (參考文獻) 30. Vasicek, O., (1977), “An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics, Vol. 5, pp. 177-88.zh_TW