學術產出-學位論文

題名 可贖回雪球式商品的評價與避險
作者 曹若玹
貢獻者 廖四郎
曹若玹
關鍵詞 利率連動債券
最小平方蒙地卡羅
參數校準
提前贖回
避險參數
BGM
LFM
LIBOR
Greeks
calibration
snowball
Sausage Monte Carlo
pathwise
日期 2005
上傳時間 17-九月-2009 19:02:32 (UTC+8)
摘要 本文採用Lognormal Forward LIBOR Model (LFM) 利率模型,針對可贖回雪球式債券進行相關的評價與避險分析,而由於此商品的計息方式為路徑相依型態,價格沒有封閉解,故必須利用數值方法來進行評價。過去通常使用二元樹或三元樹的方法來評價具有可贖回特性的商品,但因為LFM是屬於多因子模型,所以不容易處理建樹的過程。而一般路徑相依商品的評價是使用蒙地卡羅法來進行,但是標準的蒙地卡羅法不易處理美式或百慕達式選擇權的問題,因此,本研究將使用由Longstaff and Schwartz(2001)所提出的最小平方蒙地卡羅法,來處理同時具有可贖回與路徑相依特性的商品評價並進行實證研究。


此外,關於可贖回商品的避險參數部分,由於商品的價格函數不具有連續性,若在蒙地卡羅法之下直接使用重新模擬的方式來求算避險參數,將會造成不準確的結果,而Piterbarg (2004)提出了兩種可用來計算在LFM下可贖回商品避險參數的方法,其實証結果發現所求出的避險參數結果較準確,因此本研究將此方法運用至可贖回雪球式利率連動債券,並分析各種參數變化對商品價格的影響大小,便於進行避險工作。
參考文獻 [1] Brace, A., D. Gatarek and M. Musiela (1997). The Market Model of Interest Rate . Dynamics Mathematical Finance 7, 127-155.
[2] Brigo, D. and F. Mercurio (2001). Interest Models, Theory and Practice. Springer-Verlag.
[3] Carol Alexander(2003). Common Correlation and Calibrating the Lognormal Forward Rate Model . ISMA Discussion Papers in Finance 2002-18. To appear in Wilmott Magazine.
[4] Glasserman, P. (2004). Monte Carlo Method in Financial Engineering. New York,Springer.
[5] Glasserman, P., and X., Zhao (1999). Fast Greeks by Simulation in Forward LIBOR Models, Journal of Computational Finance 3, 5-39.
[6] Glasserman, P., and Yu, B.(2004). Number of Paths Versus Number of Basis Functions in American Option Pricing. Annuals of Applied Probability 14(4), 2090-2119.
[7] Jamshidian, F. (1997). LIBOR and Swap Market Models and Measures . Finance and Stochastics 1, 293-330.
[8] Longstaff, F. and Schwartz, E. (2001).Valuing American Options by Simulation: A Simple Least-Squares Approach. The Review of Financial Studies, Vol. 14, No.1, p.113-147.
[9] Piterbarg.V.V.(2003). A Practioner’s Guide to Pricing and hedging Callable Libor Exotics in Forward Libor Models, SSRN Working Paper.
[10] Piterbarg.V.V.(2004a). Computing Deltas of Callable Libor Exotics in Forward Libor Models. Journal of Computational Finance 7(3),107-144.
[11] Piterbarg.V.V.(2004b). Pricing and Hedging Callable Libor Exotics in Forward Libor Models. Journal of Computational Finance 8(2), 65-117.
[12] Rebonato, R. (1998). Interest Rate Option Models. Second Edition. Wiley, Chichester.
[13] Rebonato, R. (1999). Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options, John Wiley & Sons Ltd., West Sussex.
[14] Rebonato, R.(1999). On the Simultaneous Calibration of Multifactor Lognormal Interest Rate Models to Black Volatilities and to the Correlation Matrix, The Journal of Computational Finance,2, 5-27.
[15] Rebonato, R (2002), Modern Pricing of Interest-Rate DerivativesL:The LIBOR Market Model and Beyond. Princeton University. Press, Princeton.
[16] Schoenmakers, J. and C., Coffet (2000). Stable Implied Calibration of a Multi-factor Libor Model via a Semi-parametric Correlation Structure, Weierstress Institute Preprint no.611.
[17] Shreve, S. (2004). Stochastic Calculus for Finance II, Springer-Verlag, New York.
[18] Svoboda, S. (2004). Interest Rate Modelling , Palgrave Macmillan, New York.
描述 碩士
國立政治大學
金融研究所
93352009
94
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0093352009
資料類型 thesis
dc.contributor.advisor 廖四郎zh_TW
dc.contributor.author (作者) 曹若玹zh_TW
dc.creator (作者) 曹若玹zh_TW
dc.date (日期) 2005en_US
dc.date.accessioned 17-九月-2009 19:02:32 (UTC+8)-
dc.date.available 17-九月-2009 19:02:32 (UTC+8)-
dc.date.issued (上傳時間) 17-九月-2009 19:02:32 (UTC+8)-
dc.identifier (其他 識別碼) G0093352009en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/33991-
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) 93352009zh_TW
dc.description (描述) 94zh_TW
dc.description.abstract (摘要) 本文採用Lognormal Forward LIBOR Model (LFM) 利率模型,針對可贖回雪球式債券進行相關的評價與避險分析,而由於此商品的計息方式為路徑相依型態,價格沒有封閉解,故必須利用數值方法來進行評價。過去通常使用二元樹或三元樹的方法來評價具有可贖回特性的商品,但因為LFM是屬於多因子模型,所以不容易處理建樹的過程。而一般路徑相依商品的評價是使用蒙地卡羅法來進行,但是標準的蒙地卡羅法不易處理美式或百慕達式選擇權的問題,因此,本研究將使用由Longstaff and Schwartz(2001)所提出的最小平方蒙地卡羅法,來處理同時具有可贖回與路徑相依特性的商品評價並進行實證研究。


此外,關於可贖回商品的避險參數部分,由於商品的價格函數不具有連續性,若在蒙地卡羅法之下直接使用重新模擬的方式來求算避險參數,將會造成不準確的結果,而Piterbarg (2004)提出了兩種可用來計算在LFM下可贖回商品避險參數的方法,其實証結果發現所求出的避險參數結果較準確,因此本研究將此方法運用至可贖回雪球式利率連動債券,並分析各種參數變化對商品價格的影響大小,便於進行避險工作。
zh_TW
dc.description.tableofcontents 第一章 緒論
第一節 研究動機 ………………………………………………………7
第二節 研究目的………………………………………………………8
第三節 研究架構………………………………………………………9
第二章 文獻回顧
第一節 利率連動債券的演進…………………………………………11
第二節 利率連動債券的演… ………………………………………14
第三章 模型評價
第一節 Lognormal Forward LIBOR Model (LFM)……………20
第二節 交換利率的評價 ………………………………………………33
第三節 LFM下的近似Swaption波動度………………………………36
第四章 評價方法
第一節 蒙地卡羅模擬法 ……………………………………………42
第二節 最小平方蒙地卡羅法…………………………………………44
第三節 參數校準………………………………………………………50
第四節 避險參數(Greeks)的估計… ………………………………56
第五章 商品實例
第一節 雪球式利率連動債券 …………………………………………67
第二節 建構期初殖利率曲線…………………………………………69
第三節 校準遠期利率瞬間波動度……………………………………73
第四節 校準遠期利率瞬間相關係數…………………………………77
第五節 商品評價………………………………………………………79
第六節 商品的風險管理………………………………………………84
第六章 結論與建議
第一節 研究結論… ……………………………………………………87
第二節 建議……………………………………………………………89
參考書目…………………………………………………………………………90
附錄A ……………………………………………………………………………92
zh_TW
dc.format.extent 42814 bytes-
dc.format.extent 94658 bytes-
dc.format.extent 75362 bytes-
dc.format.extent 64145 bytes-
dc.format.extent 115608 bytes-
dc.format.extent 158879 bytes-
dc.format.extent 234156 bytes-
dc.format.extent 251599 bytes-
dc.format.extent 203133 bytes-
dc.format.extent 105221 bytes-
dc.format.extent 62500 bytes-
dc.format.extent 85844 bytes-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0093352009en_US
dc.subject (關鍵詞) 利率連動債券zh_TW
dc.subject (關鍵詞) 最小平方蒙地卡羅zh_TW
dc.subject (關鍵詞) 參數校準zh_TW
dc.subject (關鍵詞) 提前贖回zh_TW
dc.subject (關鍵詞) 避險參數zh_TW
dc.subject (關鍵詞) BGMen_US
dc.subject (關鍵詞) LFMen_US
dc.subject (關鍵詞) LIBORen_US
dc.subject (關鍵詞) Greeksen_US
dc.subject (關鍵詞) calibrationen_US
dc.subject (關鍵詞) snowballen_US
dc.subject (關鍵詞) Sausage Monte Carloen_US
dc.subject (關鍵詞) pathwiseen_US
dc.title (題名) 可贖回雪球式商品的評價與避險zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Brace, A., D. Gatarek and M. Musiela (1997). The Market Model of Interest Rate . Dynamics Mathematical Finance 7, 127-155.zh_TW
dc.relation.reference (參考文獻) [2] Brigo, D. and F. Mercurio (2001). Interest Models, Theory and Practice. Springer-Verlag.zh_TW
dc.relation.reference (參考文獻) [3] Carol Alexander(2003). Common Correlation and Calibrating the Lognormal Forward Rate Model . ISMA Discussion Papers in Finance 2002-18. To appear in Wilmott Magazine.zh_TW
dc.relation.reference (參考文獻) [4] Glasserman, P. (2004). Monte Carlo Method in Financial Engineering. New York,Springer.zh_TW
dc.relation.reference (參考文獻) [5] Glasserman, P., and X., Zhao (1999). Fast Greeks by Simulation in Forward LIBOR Models, Journal of Computational Finance 3, 5-39.zh_TW
dc.relation.reference (參考文獻) [6] Glasserman, P., and Yu, B.(2004). Number of Paths Versus Number of Basis Functions in American Option Pricing. Annuals of Applied Probability 14(4), 2090-2119.zh_TW
dc.relation.reference (參考文獻) [7] Jamshidian, F. (1997). LIBOR and Swap Market Models and Measures . Finance and Stochastics 1, 293-330.zh_TW
dc.relation.reference (參考文獻) [8] Longstaff, F. and Schwartz, E. (2001).Valuing American Options by Simulation: A Simple Least-Squares Approach. The Review of Financial Studies, Vol. 14, No.1, p.113-147.zh_TW
dc.relation.reference (參考文獻) [9] Piterbarg.V.V.(2003). A Practioner’s Guide to Pricing and hedging Callable Libor Exotics in Forward Libor Models, SSRN Working Paper.zh_TW
dc.relation.reference (參考文獻) [10] Piterbarg.V.V.(2004a). Computing Deltas of Callable Libor Exotics in Forward Libor Models. Journal of Computational Finance 7(3),107-144.zh_TW
dc.relation.reference (參考文獻) [11] Piterbarg.V.V.(2004b). Pricing and Hedging Callable Libor Exotics in Forward Libor Models. Journal of Computational Finance 8(2), 65-117.zh_TW
dc.relation.reference (參考文獻) [12] Rebonato, R. (1998). Interest Rate Option Models. Second Edition. Wiley, Chichester.zh_TW
dc.relation.reference (參考文獻) [13] Rebonato, R. (1999). Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options, John Wiley & Sons Ltd., West Sussex.zh_TW
dc.relation.reference (參考文獻) [14] Rebonato, R.(1999). On the Simultaneous Calibration of Multifactor Lognormal Interest Rate Models to Black Volatilities and to the Correlation Matrix, The Journal of Computational Finance,2, 5-27.zh_TW
dc.relation.reference (參考文獻) [15] Rebonato, R (2002), Modern Pricing of Interest-Rate DerivativesL:The LIBOR Market Model and Beyond. Princeton University. Press, Princeton.zh_TW
dc.relation.reference (參考文獻) [16] Schoenmakers, J. and C., Coffet (2000). Stable Implied Calibration of a Multi-factor Libor Model via a Semi-parametric Correlation Structure, Weierstress Institute Preprint no.611.zh_TW
dc.relation.reference (參考文獻) [17] Shreve, S. (2004). Stochastic Calculus for Finance II, Springer-Verlag, New York.zh_TW
dc.relation.reference (參考文獻) [18] Svoboda, S. (2004). Interest Rate Modelling , Palgrave Macmillan, New York.zh_TW