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題名 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
Pricing and Empirical Analysis of Callable Range Accrual Linked to CMS: Comparison of LIBOR and GARCH Market Models作者 馮冠群
Feng, Kuan-Chun貢獻者 薛慧敏<br>林士貴
Hsueh, Hui-Min<br>Lin, Shih-Kuei
馮冠群
Feng, Kuan-Chun關鍵詞 固定期限交換利率
對數常態遠期利率市場模型
GARCH 波動度模型
區間計息
最小平方蒙地卡羅法
CMS
LFM
GARCH model
Range accrual
Least squares monte carlo method日期 2018 上傳時間 27-Jul-2018 11:34:54 (UTC+8) 摘要 透過最小平方蒙地卡羅法以對數常態遠期利率(Lognormal Forward LIBOR Model, LFM)市場模型，及廣義自我回歸條件異質變異(Generalized Autoregressive Conditional Heteroscedasticity, GARCH) 波動度市場模型來評價可贖回區間計息(Range Accrual)固定期限交換利率(Constant Maturity Swap, CMS)的衍生性商品。在本研究中，由於在區間計息下無法推導出封閉解，以LFM 下的動態過程為基礎，模擬未來的市場LIBOR 利率及CMS 利率，以最小平方蒙地卡羅法評價商品。波動度估計採兩種方式，第一種以歷史資料估計，第二種將LFM 的遠期利率瞬間波動度的假設形式改以GARCH 波動度模型表示，將兩者CMS 模擬結果與真實市場價格做比較。實證結果顯示將LFM 的遠期利率瞬間波動度的假設形式改以GARCH 模型之CMS 模擬更貼近市場真實價格。
Through the least squares Monte Carlo method, Using the Lognormal Forward LIBOR Model (LFM) and GARCH (Generalized Autoregressive conditional heteroskedasticity) market models to price the derivatives of the CMS (Constant Maturity Swap) Range Accrual. In this paper, since the closed form of solution can’t be derived under the range accrual, firstly we based on the dynamic process under LFM, the forward LIBOR interest rate and CMS interest rate are simulated, and the derivatives is evaluated by the least square Monte Carlo method. There are two ways to estimate the volatility. The first one is estimated by historical data. The second is to change the hypothetical form of LFM`s forward rate instantaneous volatility to the GARCH volatility model, and the two CMS simulation results are compared with the real market price. The empirical results show that the hypothetical form of LFM`s forward interest rate instantaneous volatility which changed to the GARCH model, it’s CMS simulation is closer to the real market price.參考文獻 中文部分 1.陳松男，2008，金融工程學-金融商品創新與選擇權理論，三版，台北：新陸書局。 2.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。 3.黃貞樺，2007，LIBOR 市場模型下可贖回區間計息連動債券之評價與分析，政大金融研究所碩士論文。 英文部分 1. Andersen, T., & Bollerslev, T., 1998, “The Dynamic International Optimal Hedge Ratio”, International Journal of Econometrics and Financial Management, Vol.2,No.3, 82-94. 2. Black, F., Derman, E., & Toy, W., 1990, “A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options”, Financial Analysts Journal, 24–32. 3. Bollerslev, T., 1986, “Generalized autoregressive conditional heteroskedasticity”,Journal of Econometrics , Vol.31, 307-327. 4. Brace, A., D. Gatarek., & M. Musiela., 1997, “The Market Model of Interest Rate Dynamics”, Mathematical Finance, Vol.7, 127-155. 5. Brigo, D., & F. Mercurio., 2001, “Interest Models, Theory and Practice”. Springer-Verlag. 6. Cox, J.C., J.E. Ingersoll., & S.A. Ross., 1985, “A Theory of the Term Structure of Interest Rates”, Econometrica, Vol.53, 385–407. 7. Decaudaveine, M., 2016, “A Review of CMS Swap Pricing Approaches”, Paris Dauphine University Master Thesis. 8. Engle, R., & Kroner. F., 1995, “Multivariate simultaneous generalized ARCH”, Econometric Theory, Vol.11, 122–150. 9. Engle, R., 1982, “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation”, Econometrica, Vol.50, 987–1007. 10. Engle, R., 2002, “Dynamic conditional correlation—a simple class of multivariate GARCH models”, Journal of Business and Economic Statistics, Vol.20, 339–350. 11. F.C .Palm., 1996, “GARCH models of volatility”, Handbook of Statistics, Vol. 14,209-240. 12. Glasserman, P., 2004, “Monte Carlo Method in Financial Engineering”, New York, Springer. 13. Glasserman, P., & Yu, B., 2004, “Number of Paths Versus Number of Basis Functions in American Option Pricing”, Annuals of Applied Probability, Vol.14, No.4, 2090-2119. 14. Heath, D., Jarrow, R., & Morton, A., 1990, “Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation”, Journal of Financial and Quantitative Analysis, No.25, 419-440. 15. Ho, T.S.Y., & Lee, S.B., 1986, “Term structure movements and pricing interest rate contingent claims”, Journal of Finance, Vol.41, No.5, 1011-1029. 16. Hull, J., & White, A., 1996, “Using Hull-White interest rate trees”, Journal of Derivatives, Vol.3, No.3, 26–36. 17. Jamshidian, F., 1997, “LIBOR and Swap Market Models and Measures”, Finance and Stochastics, Vol.1, 293-330. 18. Lin, W.L., 1992, “Alternative estimators for factor GARCH models—a Monte Carlo comparison”, Journal of Applied Econometrics, Vol.7, 259–279. 19. Longstaff, F., & Schwartz, E., 2001, “Valuing American Options by Simulation: A Simple Least-Squares Approach”, The Review of Financial Studies, Vol. 14, No.1, 113-147. 20. Lu. Y & Neftci. S., 2003, “Convexity Adjustments and Forward Libor Model: Case of Constant Maturity Swaps”, Working Paper No. 115, National Centre of Competence in Research Financial Valuation and Risk Management. 21. Plesser, A., 2003, “Mathematical foundation of convexity correction”, Quantitative Finance, Vol. 3, 59-65. 22. Rebonato, R., 2002, “Modern Pricing of Interest-Rate Derivatives: The LIBOR Market Model and Beyond”, Princeton University. Press, Princeton 23. Rebonato, R., 1998, “Interest Rate Option Models”, Second Edition, Wiley, Chichester. 24. Rebonato, R., 1999, “Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options”, John Wiley & Sons Ltd., West Sussex. 25. Shreve, S., 2004, “Stochastic Calculus for Finance II”, Springer-Verlag, New York. 26. Svoboda, S., 2004, “Interest Rate Modeling”, Palgrave Macmillan, New York. 27. Tse Y.K., & Tsui A.K.C., 2002, “A multivariate GARCH model with time-varying correlations”, Journal of Business and Economic Statistics, Vol. 20, 351–362. 28. Vasicek, O., 1977, “An equilibrium characterization of the term structure”, Journal of Financial Economics, Vol. 5, No.2, 177–188. 29. Vojtek, M., 2004, “Calibration of Interest Rate Models -Transition Market Case”, Working Paper, Center for Economic Research and Graduate Education of Charles University. 描述 碩士
國立政治大學
統計學系
1053540191資料來源 http://thesis.lib.nccu.edu.tw/record/#G1053540191 資料類型 thesis dc.contributor.advisor 薛慧敏<br>林士貴 zh_TW dc.contributor.advisor Hsueh, Hui-Min<br>Lin, Shih-Kuei en_US dc.contributor.author (Authors) 馮冠群 zh_TW dc.contributor.author (Authors) Feng, Kuan-Chun en_US dc.creator (作者) 馮冠群 zh_TW dc.creator (作者) Feng, Kuan-Chun en_US dc.date (日期) 2018 en_US dc.date.accessioned 27-Jul-2018 11:34:54 (UTC+8) - dc.date.available 27-Jul-2018 11:34:54 (UTC+8) - dc.date.issued (上傳時間) 27-Jul-2018 11:34:54 (UTC+8) - dc.identifier (Other Identifiers) G1053540191 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/118936 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 1053540191 zh_TW dc.description.abstract (摘要) 透過最小平方蒙地卡羅法以對數常態遠期利率(Lognormal Forward LIBOR Model, LFM)市場模型，及廣義自我回歸條件異質變異(Generalized Autoregressive Conditional Heteroscedasticity, GARCH) 波動度市場模型來評價可贖回區間計息(Range Accrual)固定期限交換利率(Constant Maturity Swap, CMS)的衍生性商品。在本研究中，由於在區間計息下無法推導出封閉解，以LFM 下的動態過程為基礎，模擬未來的市場LIBOR 利率及CMS 利率，以最小平方蒙地卡羅法評價商品。波動度估計採兩種方式，第一種以歷史資料估計，第二種將LFM 的遠期利率瞬間波動度的假設形式改以GARCH 波動度模型表示，將兩者CMS 模擬結果與真實市場價格做比較。實證結果顯示將LFM 的遠期利率瞬間波動度的假設形式改以GARCH 模型之CMS 模擬更貼近市場真實價格。 zh_TW dc.description.abstract (摘要) Through the least squares Monte Carlo method, Using the Lognormal Forward LIBOR Model (LFM) and GARCH (Generalized Autoregressive conditional heteroskedasticity) market models to price the derivatives of the CMS (Constant Maturity Swap) Range Accrual. In this paper, since the closed form of solution can’t be derived under the range accrual, firstly we based on the dynamic process under LFM, the forward LIBOR interest rate and CMS interest rate are simulated, and the derivatives is evaluated by the least square Monte Carlo method. There are two ways to estimate the volatility. The first one is estimated by historical data. The second is to change the hypothetical form of LFM`s forward rate instantaneous volatility to the GARCH volatility model, and the two CMS simulation results are compared with the real market price. The empirical results show that the hypothetical form of LFM`s forward interest rate instantaneous volatility which changed to the GARCH model, it’s CMS simulation is closer to the real market price. en_US dc.description.tableofcontents 第一章 續論 1 第一節 研究動機 1 第二節 研究目的 1 第二章 相關文獻回顧 3 第一節 利率模型 3 第二節 LFM 模型 5 第三節 固定期限交換利率 6 第四節 GARCH 波動度模型7 第五節 LFM 結合GARCH 波動度模型 8 第三章 可贖回區間計息CMS衍生性商品評價9 第一節 遠期 LIBOR 9 第二節 交換利率13 第三節 固定期限交換利率 15 第四節 最小平方蒙地卡羅評價法18 第四章 模型參數估計 21 第一節 利率波動度結構21 第二節 相關係數估計 24 第三節 違約強度 25 第五章 實證分析27 第一節 區間計息 27 第二節 個案商品28 第六章 結論與建議 40 第一節 研究結論 40 第二節 研究建議 40 參考文獻 42 附錄 45 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1053540191 en_US dc.subject (關鍵詞) 固定期限交換利率 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) GARCH 波動度模型 zh_TW dc.subject (關鍵詞) 區間計息 zh_TW dc.subject (關鍵詞) 最小平方蒙地卡羅法 zh_TW dc.subject (關鍵詞) CMS en_US dc.subject (關鍵詞) LFM en_US dc.subject (關鍵詞) GARCH model en_US dc.subject (關鍵詞) Range accrual en_US dc.subject (關鍵詞) Least squares monte carlo method en_US dc.title (題名) 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 zh_TW dc.title (題名) Pricing and Empirical Analysis of Callable Range Accrual Linked to CMS: Comparison of LIBOR and GARCH Market Models en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 中文部分 1.陳松男，2008，金融工程學-金融商品創新與選擇權理論，三版，台北：新陸書局。 2.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。 3.黃貞樺，2007，LIBOR 市場模型下可贖回區間計息連動債券之評價與分析，政大金融研究所碩士論文。 英文部分 1. Andersen, T., & Bollerslev, T., 1998, “The Dynamic International Optimal Hedge Ratio”, International Journal of Econometrics and Financial Management, Vol.2,No.3, 82-94. 2. Black, F., Derman, E., & Toy, W., 1990, “A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options”, Financial Analysts Journal, 24–32. 3. Bollerslev, T., 1986, “Generalized autoregressive conditional heteroskedasticity”,Journal of Econometrics , Vol.31, 307-327. 4. Brace, A., D. Gatarek., & M. Musiela., 1997, “The Market Model of Interest Rate Dynamics”, Mathematical Finance, Vol.7, 127-155. 5. Brigo, D., & F. Mercurio., 2001, “Interest Models, Theory and Practice”. Springer-Verlag. 6. Cox, J.C., J.E. Ingersoll., & S.A. Ross., 1985, “A Theory of the Term Structure of Interest Rates”, Econometrica, Vol.53, 385–407. 7. Decaudaveine, M., 2016, “A Review of CMS Swap Pricing Approaches”, Paris Dauphine University Master Thesis. 8. Engle, R., & Kroner. F., 1995, “Multivariate simultaneous generalized ARCH”, Econometric Theory, Vol.11, 122–150. 9. Engle, R., 1982, “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation”, Econometrica, Vol.50, 987–1007. 10. Engle, R., 2002, “Dynamic conditional correlation—a simple class of multivariate GARCH models”, Journal of Business and Economic Statistics, Vol.20, 339–350. 11. F.C .Palm., 1996, “GARCH models of volatility”, Handbook of Statistics, Vol. 14,209-240. 12. Glasserman, P., 2004, “Monte Carlo Method in Financial Engineering”, New York, Springer. 13. Glasserman, P., & Yu, B., 2004, “Number of Paths Versus Number of Basis Functions in American Option Pricing”, Annuals of Applied Probability, Vol.14, No.4, 2090-2119. 14. Heath, D., Jarrow, R., & Morton, A., 1990, “Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation”, Journal of Financial and Quantitative Analysis, No.25, 419-440. 15. Ho, T.S.Y., & Lee, S.B., 1986, “Term structure movements and pricing interest rate contingent claims”, Journal of Finance, Vol.41, No.5, 1011-1029. 16. Hull, J., & White, A., 1996, “Using Hull-White interest rate trees”, Journal of Derivatives, Vol.3, No.3, 26–36. 17. Jamshidian, F., 1997, “LIBOR and Swap Market Models and Measures”, Finance and Stochastics, Vol.1, 293-330. 18. Lin, W.L., 1992, “Alternative estimators for factor GARCH models—a Monte Carlo comparison”, Journal of Applied Econometrics, Vol.7, 259–279. 19. Longstaff, F., & Schwartz, E., 2001, “Valuing American Options by Simulation: A Simple Least-Squares Approach”, The Review of Financial Studies, Vol. 14, No.1, 113-147. 20. Lu. Y & Neftci. S., 2003, “Convexity Adjustments and Forward Libor Model: Case of Constant Maturity Swaps”, Working Paper No. 115, National Centre of Competence in Research Financial Valuation and Risk Management. 21. Plesser, A., 2003, “Mathematical foundation of convexity correction”, Quantitative Finance, Vol. 3, 59-65. 22. Rebonato, R., 2002, “Modern Pricing of Interest-Rate Derivatives: The LIBOR Market Model and Beyond”, Princeton University. Press, Princeton 23. Rebonato, R., 1998, “Interest Rate Option Models”, Second Edition, Wiley, Chichester. 24. Rebonato, R., 1999, “Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options”, John Wiley & Sons Ltd., West Sussex. 25. Shreve, S., 2004, “Stochastic Calculus for Finance II”, Springer-Verlag, New York. 26. Svoboda, S., 2004, “Interest Rate Modeling”, Palgrave Macmillan, New York. 27. Tse Y.K., & Tsui A.K.C., 2002, “A multivariate GARCH model with time-varying correlations”, Journal of Business and Economic Statistics, Vol. 20, 351–362. 28. Vasicek, O., 1977, “An equilibrium characterization of the term structure”, Journal of Financial Economics, Vol. 5, No.2, 177–188. 29. Vojtek, M., 2004, “Calibration of Interest Rate Models -Transition Market Case”, Working Paper, Center for Economic Research and Graduate Education of Charles University. zh_TW dc.identifier.doi (DOI) 10.6814/THE.NCCU.STAT.010.2018.B03 -
