學術產出-學位論文
文章檢視/開啟
書目匯出
-
題名 隨機利率模型下台灣公債市場殖利率曲線之估計
Yield Curve Estimation Under Stochastic Interest Rate Modles :Taiwan Government Bond Market Empirical Study作者 羅家俊
Lo, Chia-Chun貢獻者 廖四郎
Liao, Szu-Lang
羅家俊
Lo, Chia-Chun關鍵詞 隨機利率
殖利率
一般動差法
台灣公債市場
stochastic interest rate
yield curve
GMM
Taiwan Government Bond Market日期 2001 上傳時間 18-四月-2016 16:27:56 (UTC+8) 摘要 隨著金融市場的開放，越來越多的金融商品被開發出來以迎合市場參予者的需求，利率衍生性金融商品是一種以利率為標的的一種新金融商品，而這種新金融商品的交易量也是相當的可觀。我們在設計金融商品的第一步就是要去定價，在現實社會中利率是隨機波動的而不是像在B-S的選擇權公式中是固定的。隨機利率模型的用途就是在描述利率隨機波動的行為，進而對利率衍生性金融商品定價。本文嘗試以隨機利率模型估計台灣公債市場的殖利率曲線，而殖利率曲線的建立對於固定收益證券及其衍生性金融商品的定價是很重要的。在台灣大部分的利率模型的研究都是利用模擬的方式做比較，這也許是因為資料取得上的問題，本文利用CKLS(1992)所提出的方式以GMM(Generalized Method of Moment)的估計方法，利用隨機利率模型估計出台灣公債市場的殖利率曲線。本文中將三種隨機利率模型做比較他們分別為: Vasicek model (Vasicek 1977),、隨機均數的Vasicek 模型 (BDFS 1998) ，以及隨機均數與隨機波動度的Vasicek 模型 (Chen,Lin 1996). 後面兩個模型是首次出現在台灣的研究文獻中。在本文的附錄中將提出如何利用偏微分方程式(PDE)的方法求解出這三個模型的零息債券價格的封閉解(Closed-Form Solution)。文中利用台灣商業本票的價格當作零息債券價格的近似值，再以RMSE (Root mean squared Price Prediction Error)作為利率模型配適公債市場價格能力的指標。本文的主要貢獻在於嘗試以隨機利率模型估計出台灣公債市場的殖利率曲線，以及介紹了兩種首次在台灣研究文獻出現的利率模型，並且詳細推導其債券價格的封閉解，這對於想要建構一個新的隨機利率模型的研究人員而言，這是一個相當好的一個練習。
With the growth in the area of financial engineering, more and more financial products are designed to meet demands of the market participants. Interest rate derivatives are those instruments whose values depend on interest rate changes. These derivatives form a huge market worth several trillions of dollars.參考文獻 Black, F., Derman, E., and Toy, W.: “A One-Factor Model of Interest Rates and its Application to Treasury Bond Options”. Financial Analysis Journal, 33-39, 1990. Balduzzi, P., S. Das, and S. Foresi, and Rangarajan K. Sundaram: “ Stochastic Mean Models of the Term Structure of Interest Rates” Advanced Fixed Income Tool. Black, F., and Karasinski, P.: “Bond and Option Pricing When Shorts are Lognormal”. Financial Analysis Journal, 47:52-59, 1991. Brennan, M.J., and Schwartz, E.S.: An “Equilibrium Model of Bond Pricing and A Test of Market Efficiency. Journal of Financial and Quantitative Analysis, 17:75-100,1982. Chan, K.C., Karolyi, G.A., Longstaff, F.A., and Sander, A.: “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate”. The Journal of Finance, 47:1209-1227 1992. Chen, Lin : “ Interest Rates Dynamics, Derivative Pricing , and Risk Management”. Springer 1996. Courtadon, G.:” The Pricing of Options on Default-free Bonds.” Journal of Financial and Quantitative Analysis. Cox, J.C., Ingersoll, J.E. and Ross, S.A. : “ A Theory of The Term Structure of Interest Rates” Econometrica, 53:385-407, 1985. Dothan, L.U.: “ On the Term Structure of Interests Rates “.Journal of Financial Economics, 6:59-69. 1978. Fong, H.G., and Vasicek , O.A.:” Fixed-Income Volatility Management.” The journal of Portfolio Management, 41-46, 1991. Gibbons, M.R., and Ramaswamy, K.: “ A test of CIR Model of Term structure”. Review of Financial Studies, 6:619-658, 1993. Heath, D., Jarrow, R.A. and Morton, A.: “Bond Pricing and the Term Structure of Interest Rates : A New Methodology for Contingent Claims Valuation.” Econometrica, 60:77-105, 1992. Ho, T.S.Y. , and Lee, S.B.,: “ Term Structure Movement and Pricing Interest Rates Contingent Claims. The Journal of Finance, 41:1011-1029, 1986. Hull, J. and White,A.: ”Pricing Interest Rates Rate Derivatives Securities” The Review of Financial Studies, 3:573-592, 1990. Hull, J. and White,A.:” Using Hull and White Interest Rates Trees” The Journal of Derivatives 26-36. 1996. Longstaff, F.A., and Schwartz, E.S.” A Two Factor Interest Rates Model and Contingent Claims Valuation”. The Journal of Fixed Income, 16-23 1992. Longstaff, F.A., and Schwartz, E.S.” Implementation of the Longstaff–Schwartz Interest Rate Model” The Journal of Fixed Income, 7-14 1992. Niraj Sinha:” An Empirical Comparison of Three Interest Rate Option Pricing Models BDT, Hull and White and HJM” A Bell and Howell Information Company 1997. Vasicek, O.: “ An Equilibrium Characterization of the Term Structure” Journal of Financial Economics, 5:177-188, 1977. Y.K Kwok :Mathematical Models of Financial Derivatives. Springer Finance 1998. 描述 碩士
國立政治大學
金融研究所
88352007資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001541 資料類型 thesis dc.contributor.advisor 廖四郎 zh_TW dc.contributor.advisor Liao, Szu-Lang en_US dc.contributor.author (作者) 羅家俊 zh_TW dc.contributor.author (作者) Lo, Chia-Chun en_US dc.creator (作者) 羅家俊 zh_TW dc.creator (作者) Lo, Chia-Chun en_US dc.date (日期) 2001 en_US dc.date.accessioned 18-四月-2016 16:27:56 (UTC+8) - dc.date.available 18-四月-2016 16:27:56 (UTC+8) - dc.date.issued (上傳時間) 18-四月-2016 16:27:56 (UTC+8) - dc.identifier (其他 識別碼) A2002001541 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85398 - 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) 88352007 zh_TW dc.description.abstract (摘要) 隨著金融市場的開放，越來越多的金融商品被開發出來以迎合市場參予者的需求，利率衍生性金融商品是一種以利率為標的的一種新金融商品，而這種新金融商品的交易量也是相當的可觀。我們在設計金融商品的第一步就是要去定價，在現實社會中利率是隨機波動的而不是像在B-S的選擇權公式中是固定的。隨機利率模型的用途就是在描述利率隨機波動的行為，進而對利率衍生性金融商品定價。本文嘗試以隨機利率模型估計台灣公債市場的殖利率曲線，而殖利率曲線的建立對於固定收益證券及其衍生性金融商品的定價是很重要的。在台灣大部分的利率模型的研究都是利用模擬的方式做比較，這也許是因為資料取得上的問題，本文利用CKLS(1992)所提出的方式以GMM(Generalized Method of Moment)的估計方法，利用隨機利率模型估計出台灣公債市場的殖利率曲線。本文中將三種隨機利率模型做比較他們分別為: Vasicek model (Vasicek 1977),、隨機均數的Vasicek 模型 (BDFS 1998) ，以及隨機均數與隨機波動度的Vasicek 模型 (Chen,Lin 1996). 後面兩個模型是首次出現在台灣的研究文獻中。在本文的附錄中將提出如何利用偏微分方程式(PDE)的方法求解出這三個模型的零息債券價格的封閉解(Closed-Form Solution)。文中利用台灣商業本票的價格當作零息債券價格的近似值，再以RMSE (Root mean squared Price Prediction Error)作為利率模型配適公債市場價格能力的指標。本文的主要貢獻在於嘗試以隨機利率模型估計出台灣公債市場的殖利率曲線，以及介紹了兩種首次在台灣研究文獻出現的利率模型，並且詳細推導其債券價格的封閉解，這對於想要建構一個新的隨機利率模型的研究人員而言，這是一個相當好的一個練習。 zh_TW dc.description.abstract (摘要) With the growth in the area of financial engineering, more and more financial products are designed to meet demands of the market participants. Interest rate derivatives are those instruments whose values depend on interest rate changes. These derivatives form a huge market worth several trillions of dollars. en_US dc.description.tableofcontents 封面頁 證明書 致謝詞 論文摘要 目錄 表目錄 圖目錄 1. INTRODUCTION 1.1 The Relationship Among Bond prices, Bond Yields, Forward Rates and Short Rates 1.1.1 Bond Yields 1.1.2 Pure Discount Bonds 1.1.3 Forward Rates 1.1.4 Short Rates 1.2 Motivation for This Research 2. A SURVEY OF INTEREST RATE PRICING MODELD 2.1 Classifying Interest Rate Models 2.2 Single Factor Models 2.3 Two Factors Models 2.4 Yield Curves Models 3. MODELS DESCRIBTION 3.1 Vasicek Model 3.2 Stochastic Mean Model 3.3 Stochastic Mean and Volatility Model 4. ECNOMETRICS 4.1 GMM Estimation 4.1.1 Example: Chan, Karolyi, Longstaff and Sanders 4.1.2 Over-Estimation and Weighting Matrix 4.2 Apply GMM in Our Models 4.2.1 Apply GMM in Two-Factors Model 4.2.2 Apply GMM in Three-Factors Model 5. DATA AND EMPIRICAL RESULTS 5.1 DATA 5.2 Parameters Estimation 5.3 Yield Curve Constructed 6. CONCLUSION APPENDIX APPENDIX A Derive Vasicek Model’s Zero Coupon Bond Formula APPENDIX B Derive Stochastic Mean Model’s Zero Coupon Bond Formula APPENDIX C Derive Stochastic Mean and Stochastic Volatility Model’s Zero Coupon Bond Formula APPENDIX D The Difference Between the Thirty Days Rates and our Estimated Stochastic Long Mean of the Three Factors Model Reference zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001541 en_US dc.subject (關鍵詞) 隨機利率 zh_TW dc.subject (關鍵詞) 殖利率 zh_TW dc.subject (關鍵詞) 一般動差法 zh_TW dc.subject (關鍵詞) 台灣公債市場 zh_TW dc.subject (關鍵詞) stochastic interest rate en_US dc.subject (關鍵詞) yield curve en_US dc.subject (關鍵詞) GMM en_US dc.subject (關鍵詞) Taiwan Government Bond Market en_US dc.title (題名) 隨機利率模型下台灣公債市場殖利率曲線之估計 zh_TW dc.title (題名) Yield Curve Estimation Under Stochastic Interest Rate Modles :Taiwan Government Bond Market Empirical Study en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Black, F., Derman, E., and Toy, W.: “A One-Factor Model of Interest Rates and its Application to Treasury Bond Options”. Financial Analysis Journal, 33-39, 1990. Balduzzi, P., S. Das, and S. Foresi, and Rangarajan K. Sundaram: “ Stochastic Mean Models of the Term Structure of Interest Rates” Advanced Fixed Income Tool. Black, F., and Karasinski, P.: “Bond and Option Pricing When Shorts are Lognormal”. Financial Analysis Journal, 47:52-59, 1991. Brennan, M.J., and Schwartz, E.S.: An “Equilibrium Model of Bond Pricing and A Test of Market Efficiency. Journal of Financial and Quantitative Analysis, 17:75-100,1982. Chan, K.C., Karolyi, G.A., Longstaff, F.A., and Sander, A.: “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate”. The Journal of Finance, 47:1209-1227 1992. Chen, Lin : “ Interest Rates Dynamics, Derivative Pricing , and Risk Management”. Springer 1996. Courtadon, G.:” The Pricing of Options on Default-free Bonds.” Journal of Financial and Quantitative Analysis. Cox, J.C., Ingersoll, J.E. and Ross, S.A. : “ A Theory of The Term Structure of Interest Rates” Econometrica, 53:385-407, 1985. Dothan, L.U.: “ On the Term Structure of Interests Rates “.Journal of Financial Economics, 6:59-69. 1978. Fong, H.G., and Vasicek , O.A.:” Fixed-Income Volatility Management.” The journal of Portfolio Management, 41-46, 1991. Gibbons, M.R., and Ramaswamy, K.: “ A test of CIR Model of Term structure”. Review of Financial Studies, 6:619-658, 1993. Heath, D., Jarrow, R.A. and Morton, A.: “Bond Pricing and the Term Structure of Interest Rates : A New Methodology for Contingent Claims Valuation.” Econometrica, 60:77-105, 1992. Ho, T.S.Y. , and Lee, S.B.,: “ Term Structure Movement and Pricing Interest Rates Contingent Claims. The Journal of Finance, 41:1011-1029, 1986. Hull, J. and White,A.: ”Pricing Interest Rates Rate Derivatives Securities” The Review of Financial Studies, 3:573-592, 1990. Hull, J. and White,A.:” Using Hull and White Interest Rates Trees” The Journal of Derivatives 26-36. 1996. Longstaff, F.A., and Schwartz, E.S.” A Two Factor Interest Rates Model and Contingent Claims Valuation”. The Journal of Fixed Income, 16-23 1992. Longstaff, F.A., and Schwartz, E.S.” Implementation of the Longstaff–Schwartz Interest Rate Model” The Journal of Fixed Income, 7-14 1992. Niraj Sinha:” An Empirical Comparison of Three Interest Rate Option Pricing Models BDT, Hull and White and HJM” A Bell and Howell Information Company 1997. Vasicek, O.: “ An Equilibrium Characterization of the Term Structure” Journal of Financial Economics, 5:177-188, 1977. Y.K Kwok :Mathematical Models of Financial Derivatives. Springer Finance 1998. zh_TW
