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題名 可贖回CMS價差區間計息型商品之評價分析：基於LFM與最小平方蒙地卡羅法之模擬加速實證
Pricing of Callable Range Accrual Linked to CMS Spread: Empirical Analysis with Multiprocessing Based on Lognormal Forward LIBOR Model and Least-Squares Monte Carlo Simulation作者 王韋之
Wang, Wei-Chih貢獻者 林士貴<br>岳夢蘭
Lin, Shih-Kuei<br>Yueh, Meng-Lan
王韋之
Wang, Wei-Chih關鍵詞 利率衍生性商品
對數常態遠期利率市場模型
固定期限交換利率
最小平方蒙地卡羅法
平行運算
Interest Rate Derivative
Lognormal Forward LIBOR Model
Constant Maturity Swap
Least-Squares Monte Carlo Simulation
Multiprocessing日期 2020 上傳時間 1-Jul-2020 13:41:12 (UTC+8) 摘要 本研究使用對數常態遠期利率市場模型與最小平方蒙地卡羅法，對沒有封閉解之可贖回固定期限交換利率價差區間計息商品進行評價。透過市場資料建構殖利率曲線與遠期利率曲線，而後基於對數常態遠期利率市場模型之動態過程，將其離散化後進行遠期利率模擬並計算遠期交換利率，最後使用最小平方蒙地卡羅法求解商品價值。本研究利用市場資料估計校準參數，基於兩種波動度結構與兩種實務上常用之相關係數假設進行模擬。此外，在結合Python平行運算的基礎上，整體的評價計算與模擬速度得到較大提升。
In this paper, we apply Lognormal Forward LIBOR Model (LFM) and Least-Squares Monte Carlo simulation (LSMC) to price the Constant Maturity Swap (CMS) Spread Range Accruals, which have no closed form solution. We build the yield curve and forward rate curve with market data. Based on the dynamic process under LFM, we discretize the formula to calculate forward rate and forward swap rate. And the derivatives are evaluated by using Least-Squares Monte Carlo method. The parameters are estimated with two types of volatility assumptions and two types of correlation assumptions based on the practical experience. Besides, combined with multiprocessing, the speed of valuation and simulation has been greatly increased.參考文獻 中文部分陳松男 (2006)。利率金融工程學-理論模型及實務應用。台北：新陸書局。陳威光 (2010)。衍生性商品：選擇權、期貨、交換與風險管理。台北：智勝文化馮冠群 (2018)。可贖回CMS區間計息型商品之評價與實證分析：LIBOR與GARCH市場模型之比較。國立政治大學統計研究所碩士論文，未出版。英文部分Andersen, L. B. (1999). A simple approach to the pricing of Bermudan swaptions in the multi-factor Libor market model.Andersen, L. B., & Brotherton-Ratcliffe, R. (2001). Extended LIBOR market models with stochastic volatility.Boyle, P. P. (1977). Options: A monte carlo approach. Journal of financial economics, 4(3), 323-338.Brigo, D., Capitani, C., & Mercurio, F. (2001). On the joint calibration of the Libor market model to caps and swaptions market volatilities.Brigo, D., & Liinev, J. (2002). On the distributional distance between the Libor and the Swap market models. Preprint.Brigo, D., & Mercurio, F. (2007). Interest rate models-theory and practice: with smile, inflation and credit. Springer Science & Business Media.Gatarek, D. (2003). Calibration of the LIBOR market model: three prescriptions.Goschen, W. S. (2005). Incompatibility of lognormal forward-Libor and Swap market models. University of Cape Town,Hull, J., & White, A. (1988). The use of the control variate technique in option pricing. Journal of Financial and Quantitative analysis, 23(3), 237-251.Hull, J. C., & White, A. D. (2000). Forward rate volatilities, swap rate volatilities, and implementation of the LIBOR market model. The Journal of Fixed Income, 10(2), 46-62.Jamshidian, F. (1997). LIBOR and swap market models and measures. Finance and Stochastics, 1(4), 293-330.Joshi, M. S., & Kwon, O. K. (2010). Monte Carlo market Greeks in the displaced diffusion LIBOR market model.13. Longstaff, F.A., & Schwartz, E.S. (2001). Valuing American options by simulation: a simple least-squares approach. The review of financial studies, 14(1), 113-147.Mercurio, F. (2010). LIBOR market models with stochastic basis. Bloomberg education and quantitative research paper(2010-05).Moreno, M., & Navas, J. F. (2003). On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Review of Derivatives Research, 6(2), 107-128.Pietersz, R. (2003). The LIBOR market model. Universität Leiden.Piterbarg, V. (2003). Computing deltas of callable LIBOR exotics in forward LIBOR models.Piterbarg, V. V. (2003). A practitioner’s guide to pricing and hedging callable LIBOR exotics in forward LIBOR models. Preprint. 描述 碩士
國立政治大學
金融學系
107352012資料來源 http://thesis.lib.nccu.edu.tw/record/#G0107352012 資料類型 thesis dc.contributor.advisor 林士貴<br>岳夢蘭 zh_TW dc.contributor.advisor Lin, Shih-Kuei<br>Yueh, Meng-Lan en_US dc.contributor.author (Authors) 王韋之 zh_TW dc.contributor.author (Authors) Wang, Wei-Chih en_US dc.creator (作者) 王韋之 zh_TW dc.creator (作者) Wang, Wei-Chih en_US dc.date (日期) 2020 en_US dc.date.accessioned 1-Jul-2020 13:41:12 (UTC+8) - dc.date.available 1-Jul-2020 13:41:12 (UTC+8) - dc.date.issued (上傳時間) 1-Jul-2020 13:41:12 (UTC+8) - dc.identifier (Other Identifiers) G0107352012 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/130542 - 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) 107352012 zh_TW dc.description.abstract (摘要) 本研究使用對數常態遠期利率市場模型與最小平方蒙地卡羅法，對沒有封閉解之可贖回固定期限交換利率價差區間計息商品進行評價。透過市場資料建構殖利率曲線與遠期利率曲線，而後基於對數常態遠期利率市場模型之動態過程，將其離散化後進行遠期利率模擬並計算遠期交換利率，最後使用最小平方蒙地卡羅法求解商品價值。本研究利用市場資料估計校準參數，基於兩種波動度結構與兩種實務上常用之相關係數假設進行模擬。此外，在結合Python平行運算的基礎上，整體的評價計算與模擬速度得到較大提升。 zh_TW dc.description.abstract (摘要) In this paper, we apply Lognormal Forward LIBOR Model (LFM) and Least-Squares Monte Carlo simulation (LSMC) to price the Constant Maturity Swap (CMS) Spread Range Accruals, which have no closed form solution. We build the yield curve and forward rate curve with market data. Based on the dynamic process under LFM, we discretize the formula to calculate forward rate and forward swap rate. And the derivatives are evaluated by using Least-Squares Monte Carlo method. The parameters are estimated with two types of volatility assumptions and two types of correlation assumptions based on the practical experience. Besides, combined with multiprocessing, the speed of valuation and simulation has been greatly increased. en_US dc.description.tableofcontents 第一章 緒論 1第一節 研究動機 1第二節 研究目的 1第二章 文獻回顧 2第一節 利率模型 2第二節 參數估計 5第三節 最小平方蒙地卡羅法 9第三章 研究方法 12第一節 遠期利率 12第二節 LFM建構遠期利率 16第三節 參數假設與估計校準 18第四節 最小平方蒙地卡羅法 20第五節 基於CPU之加速模擬 22第四章 實證分析 26第一節 USD CMS Spread Range Accrual 26第二節 模擬加速實證 43第五章 結論與展望 45第一節 研究結論 45第二節 未來展望 46參考文獻 47 zh_TW dc.format.extent 1372345 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0107352012 en_US dc.subject (關鍵詞) 利率衍生性商品 zh_TW dc.subject (關鍵詞) 對數常態遠期利率市場模型 zh_TW dc.subject (關鍵詞) 固定期限交換利率 zh_TW dc.subject (關鍵詞) 最小平方蒙地卡羅法 zh_TW dc.subject (關鍵詞) 平行運算 zh_TW dc.subject (關鍵詞) Interest Rate Derivative en_US dc.subject (關鍵詞) Lognormal Forward LIBOR Model en_US dc.subject (關鍵詞) Constant Maturity Swap en_US dc.subject (關鍵詞) Least-Squares Monte Carlo Simulation en_US dc.subject (關鍵詞) Multiprocessing en_US dc.title (題名) 可贖回CMS價差區間計息型商品之評價分析：基於LFM與最小平方蒙地卡羅法之模擬加速實證 zh_TW dc.title (題名) Pricing of Callable Range Accrual Linked to CMS Spread: Empirical Analysis with Multiprocessing Based on Lognormal Forward LIBOR Model and Least-Squares Monte Carlo Simulation en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 中文部分陳松男 (2006)。利率金融工程學-理論模型及實務應用。台北：新陸書局。陳威光 (2010)。衍生性商品：選擇權、期貨、交換與風險管理。台北：智勝文化馮冠群 (2018)。可贖回CMS區間計息型商品之評價與實證分析：LIBOR與GARCH市場模型之比較。國立政治大學統計研究所碩士論文，未出版。英文部分Andersen, L. B. (1999). A simple approach to the pricing of Bermudan swaptions in the multi-factor Libor market model.Andersen, L. B., & Brotherton-Ratcliffe, R. (2001). Extended LIBOR market models with stochastic volatility.Boyle, P. P. (1977). Options: A monte carlo approach. Journal of financial economics, 4(3), 323-338.Brigo, D., Capitani, C., & Mercurio, F. (2001). On the joint calibration of the Libor market model to caps and swaptions market volatilities.Brigo, D., & Liinev, J. (2002). On the distributional distance between the Libor and the Swap market models. Preprint.Brigo, D., & Mercurio, F. (2007). Interest rate models-theory and practice: with smile, inflation and credit. Springer Science & Business Media.Gatarek, D. (2003). Calibration of the LIBOR market model: three prescriptions.Goschen, W. S. (2005). Incompatibility of lognormal forward-Libor and Swap market models. University of Cape Town,Hull, J., & White, A. (1988). The use of the control variate technique in option pricing. Journal of Financial and Quantitative analysis, 23(3), 237-251.Hull, J. C., & White, A. D. (2000). Forward rate volatilities, swap rate volatilities, and implementation of the LIBOR market model. The Journal of Fixed Income, 10(2), 46-62.Jamshidian, F. (1997). LIBOR and swap market models and measures. Finance and Stochastics, 1(4), 293-330.Joshi, M. S., & Kwon, O. K. (2010). Monte Carlo market Greeks in the displaced diffusion LIBOR market model.13. Longstaff, F.A., & Schwartz, E.S. (2001). Valuing American options by simulation: a simple least-squares approach. The review of financial studies, 14(1), 113-147.Mercurio, F. (2010). LIBOR market models with stochastic basis. Bloomberg education and quantitative research paper(2010-05).Moreno, M., & Navas, J. F. (2003). On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Review of Derivatives Research, 6(2), 107-128.Pietersz, R. (2003). The LIBOR market model. Universität Leiden.Piterbarg, V. (2003). Computing deltas of callable LIBOR exotics in forward LIBOR models.Piterbarg, V. V. (2003). A practitioner’s guide to pricing and hedging callable LIBOR exotics in forward LIBOR models. Preprint. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202000618 en_US
