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題名 LMM利率模型下可取消利率交換評價與風險管理
Cancelable Swap Pricing and Risk Management under LIBOR Market Model作者 廖家揚
Liao, Chia Yang貢獻者 廖四郎
Liao, Szu Lang
廖家揚
Liao, Chia Yang關鍵詞 可取消利率交換
百慕達利率交換選擇權
市場利率模型
最小平方蒙地卡羅法
敏感度分析
風險值
Cancellable Swap
Bermudan Swaption
Libor Market Model
Least Squares Monte Carlo Method
Sensitivity Analysis
Value at Risk日期 2014 上傳時間 1-Jul-2015 14:45:33 (UTC+8) 摘要 許多公司在發行公司債的時候，會給此公司債一個可提前贖回的特性，此種公司債稱為可贖回公司債(Callable Bond)，用來規避利率變動風險的金融商品也與我們熟知的利率交換不同，稱為可取消利率交換(Cancelable Swap)。其實可取消利率交換可以拆解成百慕達利率交換選擇權(Bermudan Swaption)加上利率交換，由於利率交換之評價較簡單也有市場一致的評價方法，因此百慕達利率交換選擇權便成為評價的重點。 評價的部分，由於百慕達式的商品有提前履約的特性，造成其封閉解不存在，因此需要利用其他的近似解或是數值方法來求它的價格。由於本文採用BGM(1997)的市場利率模型(Libor Market Model)，其高維度的性質導致數狀方法與有限差分法使用起來較無效率，因此本文選擇使用蒙地卡羅法做為評價的方法，同時利用Longstaff and Schwartz(2001)的最小平方蒙地卡羅法(Least Squares Monte Carlo Method)來解決提前履約的問題。 最後，本文將採用2種利率波動度假設與2種不同利率間相關係數的假設，共4種組合，在歐式利率交換選擇權的市場波動度下進行校準，使用校準出來的參數進行評價來得到4種價格。再進行商品的敏感度分析(Sensitivity Analysis)和風險值(Value at Risk)的計算。 參考文獻 中文文獻[1] 王祥帆 (2005) 百慕達式利率交換選擇權。[2] 蔡宏彬 (2009) 在BGM模型下固定交換利率商品之效率避險與評價。英文文獻[1] Alpsten, H., (2003), Pricing bermudan swap options using the BGM model with arbitrage – free discretisation and boundary based option exercise, Working paper, Department of mathematics royal institute of technology.[2] Andersen, L., (2000), A Simple Approach to the Pricing of Bermudan Swaptions in the Multi – Factor Libor Market Model, Journal of Computational Finance 3(2), 1-32.[3] Brace, A., D. Gatarek, and M. Musiela, (1997), The market model of interest rate dynamics, Mathematical Finance 7(2), 127-155.[4] Brigo, D. and Mercurio, F. (2007). Interest rate models, theory and practice, Springer Science + Business Media.[5] Cox, J., Ingersoll J. and Ross, S. A theory of the term structure of interest rates, Econometrica, 53(2) (1985) 385-407.[6] Coffey, C. and Schoenmakers, J(2002). Systematic generation of parametric correlation structures for the libor market model, International Journal of Theoretical and Applied Finance.[7] Glasserman, P. (2004). Monte carlo methods in financial engineering, Springer Science + Business Media.[8] Hull, J., White, A. (1993). One-factor interest rate models and the valuation of interest rate derivative securities. Journal of Financial and Quantitative Analysis 28, 235-254. [9] Jorion, P. (1997): Value at Risk – The New Benchmark for Controlling Market Risk. McGraw-Hill, New York[10] Lvov, D. (2005). Monte carlo methods for pricing and hedging: Applications to bermudan swaptions and convertible bonds, PhD dissertation, ISMA Centre, University of Reading.[11] Longstaff, F. A., and Schwartz, E. S. (2001), “Valuing American Potions by Simulation: A Simple Least – Squares Approach”, The Review of Financial Studies 14(1), 113-147. [12] Pedersen, M. B, (1999), Bermudan Swaptions in the LIBOR market model, Financial Research Department, Preprint.[13] Pietersz, R. and A. Pelsser, (2003), Risk managing bermudan swaptions in the LIBOR BGM Model, Preprint.[14] Piterbarg, V. (2005). A practitioner’s guide to pricing and hedging callable libor exotics in forward libor models, Working paper.[15] Rebonato, R. (2002). Modern pricing of interest rate derivatives: The libor market model and beyond, Princeton University Press.[16] Steffen Hippler, (2008). Pricing bermudan swaptions in the LIBOR market model, master dissertation, university of Oxford.[17] Svoboda, S., (2004), Interest rate modelling, published by Palgrave Macmillan.[18] Tavella, D., (2002), Quantitative methods in derivatives pricing: An Introduction to Computational Finance, Published by John Wiley & Sons, Ltd.[19] Vasicek, O. (1997), An equilibrium characterization of the term structure, Journal of Financial Economics 5, 177-188.[20] Weigel, P., (2004), Optimal calibration of LIBOR market models to correlations, The Journal of Derivatives, Winter 2004, 43-50. 描述 碩士
國立政治大學
金融研究所
102352014
103資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102352014 資料類型 thesis dc.contributor.advisor 廖四郎 zh_TW dc.contributor.advisor Liao, Szu Lang en_US dc.contributor.author (Authors) 廖家揚 zh_TW dc.contributor.author (Authors) Liao, Chia Yang en_US dc.creator (作者) 廖家揚 zh_TW dc.creator (作者) Liao, Chia Yang en_US dc.date (日期) 2014 en_US dc.date.accessioned 1-Jul-2015 14:45:33 (UTC+8) - dc.date.available 1-Jul-2015 14:45:33 (UTC+8) - dc.date.issued (上傳時間) 1-Jul-2015 14:45:33 (UTC+8) - dc.identifier (Other Identifiers) G0102352014 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/76173 - 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) 102352014 zh_TW dc.description (描述) 103 zh_TW dc.description.abstract (摘要) 許多公司在發行公司債的時候，會給此公司債一個可提前贖回的特性，此種公司債稱為可贖回公司債(Callable Bond)，用來規避利率變動風險的金融商品也與我們熟知的利率交換不同，稱為可取消利率交換(Cancelable Swap)。其實可取消利率交換可以拆解成百慕達利率交換選擇權(Bermudan Swaption)加上利率交換，由於利率交換之評價較簡單也有市場一致的評價方法，因此百慕達利率交換選擇權便成為評價的重點。 評價的部分，由於百慕達式的商品有提前履約的特性，造成其封閉解不存在，因此需要利用其他的近似解或是數值方法來求它的價格。由於本文採用BGM(1997)的市場利率模型(Libor Market Model)，其高維度的性質導致數狀方法與有限差分法使用起來較無效率，因此本文選擇使用蒙地卡羅法做為評價的方法，同時利用Longstaff and Schwartz(2001)的最小平方蒙地卡羅法(Least Squares Monte Carlo Method)來解決提前履約的問題。 最後，本文將採用2種利率波動度假設與2種不同利率間相關係數的假設，共4種組合，在歐式利率交換選擇權的市場波動度下進行校準，使用校準出來的參數進行評價來得到4種價格。再進行商品的敏感度分析(Sensitivity Analysis)和風險值(Value at Risk)的計算。 zh_TW dc.description.tableofcontents 1. 緒論……………………………………………………………………………….12. 文獻回顧…………………………………………………………………………5 2.1 利率模型…………………………………………………………………..5 2.2 研究方法……………….………………………………………………….73. 模型設定………………………..………..………………………………………9 3.1市場利率模型………………………………………………….………..…9 3.2 利率交換與利率交換選擇權……………………….……………………12 3.3 最小平方蒙地卡羅法...……………………………….…………………14 3.4 Rebonato’s formula………………………………………………………16 3.5 參數模型設定…………………………………………………………….17 3.6參數校準……………………………………………………….…………19 3.7 敏感度分析與避險探討………………………………………………….22 3.8 風險值…………………………………………………………………….244. 數值結果………………………………………………………..………………27 4.1 歐式利率交換選擇權…………………………………………………….27 4.2百慕達利率交換選擇權….………………………………………...……315. 敏感度分析與風險值實證………………………………………………33 5.1 敏感度分析與避險分析…………………………………….……………345.2 風險值實證…………………………………………………….…………376. 結論……………………………………………………………………...………38參考文獻……………………………………………………………………………40中文文獻………………………………………………………………………40英文文獻………………………………………………………………………40 zh_TW dc.format.extent 919841 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102352014 en_US dc.subject (關鍵詞) 可取消利率交換 zh_TW dc.subject (關鍵詞) 百慕達利率交換選擇權 zh_TW dc.subject (關鍵詞) 市場利率模型 zh_TW dc.subject (關鍵詞) 最小平方蒙地卡羅法 zh_TW dc.subject (關鍵詞) 敏感度分析 zh_TW dc.subject (關鍵詞) 風險值 zh_TW dc.subject (關鍵詞) Cancellable Swap en_US dc.subject (關鍵詞) Bermudan Swaption en_US dc.subject (關鍵詞) Libor Market Model en_US dc.subject (關鍵詞) Least Squares Monte Carlo Method en_US dc.subject (關鍵詞) Sensitivity Analysis en_US dc.subject (關鍵詞) Value at Risk en_US dc.title (題名) LMM利率模型下可取消利率交換評價與風險管理 zh_TW dc.title (題名) Cancelable Swap Pricing and Risk Management under LIBOR Market Model en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 中文文獻[1] 王祥帆 (2005) 百慕達式利率交換選擇權。[2] 蔡宏彬 (2009) 在BGM模型下固定交換利率商品之效率避險與評價。英文文獻[1] Alpsten, H., (2003), Pricing bermudan swap options using the BGM model with arbitrage – free discretisation and boundary based option exercise, Working paper, Department of mathematics royal institute of technology.[2] Andersen, L., (2000), A Simple Approach to the Pricing of Bermudan Swaptions in the Multi – Factor Libor Market Model, Journal of Computational Finance 3(2), 1-32.[3] Brace, A., D. Gatarek, and M. Musiela, (1997), The market model of interest rate dynamics, Mathematical Finance 7(2), 127-155.[4] Brigo, D. and Mercurio, F. (2007). Interest rate models, theory and practice, Springer Science + Business Media.[5] Cox, J., Ingersoll J. and Ross, S. A theory of the term structure of interest rates, Econometrica, 53(2) (1985) 385-407.[6] Coffey, C. and Schoenmakers, J(2002). Systematic generation of parametric correlation structures for the libor market model, International Journal of Theoretical and Applied Finance.[7] Glasserman, P. (2004). Monte carlo methods in financial engineering, Springer Science + Business Media.[8] Hull, J., White, A. (1993). One-factor interest rate models and the valuation of interest rate derivative securities. Journal of Financial and Quantitative Analysis 28, 235-254. [9] Jorion, P. (1997): Value at Risk – The New Benchmark for Controlling Market Risk. McGraw-Hill, New York[10] Lvov, D. (2005). Monte carlo methods for pricing and hedging: Applications to bermudan swaptions and convertible bonds, PhD dissertation, ISMA Centre, University of Reading.[11] Longstaff, F. A., and Schwartz, E. S. (2001), “Valuing American Potions by Simulation: A Simple Least – Squares Approach”, The Review of Financial Studies 14(1), 113-147. [12] Pedersen, M. B, (1999), Bermudan Swaptions in the LIBOR market model, Financial Research Department, Preprint.[13] Pietersz, R. and A. Pelsser, (2003), Risk managing bermudan swaptions in the LIBOR BGM Model, Preprint.[14] Piterbarg, V. (2005). A practitioner’s guide to pricing and hedging callable libor exotics in forward libor models, Working paper.[15] Rebonato, R. (2002). Modern pricing of interest rate derivatives: The libor market model and beyond, Princeton University Press.[16] Steffen Hippler, (2008). Pricing bermudan swaptions in the LIBOR market model, master dissertation, university of Oxford.[17] Svoboda, S., (2004), Interest rate modelling, published by Palgrave Macmillan.[18] Tavella, D., (2002), Quantitative methods in derivatives pricing: An Introduction to Computational Finance, Published by John Wiley & Sons, Ltd.[19] Vasicek, O. (1997), An equilibrium characterization of the term structure, Journal of Financial Economics 5, 177-188.[20] Weigel, P., (2004), Optimal calibration of LIBOR market models to correlations, The Journal of Derivatives, Winter 2004, 43-50. zh_TW
