短期利率在財務理論與實證佔有相當重要的地位，利率變動會影響金融商品的價格行為，因此明瞭短期利率之動態行為將有助於金融商品之風險管理。本論文由三篇文章構成，利用台灣商業本票初級市場發行利率，由實證角度探討台灣短期利率之動態行為。
第一篇使用不同的計量技巧估計並比較連續短期利率模型在台灣短期利率之實證表現。在參數估計方面，使用兩種近似方式將連續的利率過程寫成間斷模型，再以一般動差法(GMM)與準最大概似法(QML)估計，以評估模型在資料配適上的優劣；此外，亦比較不同資料頻率(月、週資料)對模型估計與評估是否有顯著的不同。實證結果指出，不同近似方法所得到的估計結果並無太大差異，不過估計方法與資料頻率會影響估計結果，使用週資料並以準最大概似法估計所得到之結果較具穩定性與效率性；其次，台灣短期利率存在均數復歸現象，且短期利率波動性受利率水準值影響，惟敏感度係數估計值小於1，而在模型評估方面，相較於一般化的未受限制模型，以CIR-SR模型在資料的配適上表現最好。
第二篇則由樣本外預測準確性與預測涵蓋性角度，比較連續時間短期利率模型在預測台灣利率水準值與波動性的表現。在樣本外預測方面，採用遞迴迴歸方式，計算不同預測長度的利率水準值與波動性之預測值。為衡量模型預測誤差間之差異是否具有統計上的顯著性，本文採用預測準確性檢定與預測涵蓋性檢定，以評估模型樣本外的預測績效，同時，為求檢定的穩健性，分別考慮不同期間下之預測績效。實證結果發現，利率模型在樣本內/外的表現不甚相同。較複雜的模型在樣本內有優異的配適表現，然在樣本外預測表現則不盡相同。在預測利率平均數方面，有均數復歸的模型，在某些期間內表現較佳；而設定 的異質變異數模型，在預測利率波動性上，於某些期間內，表現優於同質變異數模型；至於其它形式的異質變異數模型，預測表現均不如同質變異數模型。
第三篇則針對實證上尚未有定論之利率波動性設定做探討，估計並檢定三大類利率波動模型，分別為確定的波動模型、隨機的波動模型與狀態轉換的波動模型，希冀由實證資料決定最適合的波動形式。實證結果顯示，台灣資料存在均數復歸的現象與水準效果。但以模型而言，同時考慮GARCH效果與水準效果之模型較適合台灣的資料。

This study includes three issues about the dynamic of 30-days Taiwan Commercial Paper rate (CP2).The first issue focuses on the estimation of continuous-time short-term interest rate models. We discretize the continuous-time models by using two different approaches, and then use weekly and monthly data to estimate the parameters. The models are evaluated by data fit. We find that the estimated parameters are similar for different discretization approaches and would be more stable and efficient under quasi-maximum likelihood (QML) with weekly data. There exists mean reversion for Taiwan CP rate and the relationship between the volatility and the level of interest rates are less than 1 and smaller than that of American T-Bill rates reported by CKLS (1992) and Nowman (1997). We also find that CIR-SR model performs best for Taiwan CP rate.
The second issue compares the continuous-time short-term interest rate models empirically both by predictive accuracy test and encompassing test. Having the estimated parameters of the models by discretization of Nowman(1997) and QML, we produce the forecasts on conditional mean and volatility for the interest rate over multiple-step-ahead horizons. The results indicate that the sophisticated models outperform the simpler models in the in-sample data fit, but have a distinct performance in the out-of-sample forecasting. The models equipped with mean reversion can produce better forecasts on conditional means during some period, and the heteroskedasticity variance model with outperform counterparts in volatility forecasting in some periods.
The third issue concerns the persistent and massive volatility of short-term interest rates. This part inquires how the realizations on Taiwan short-term interest rates can be best described empirically. Various popular volatility specifications are estimated and tested. The empirical findings reveal that the mean reversion is an important characteristic for the Taiwan interest rates, and the level effect exists. Overall, the GARCH-L model fits well to Taiwan interest rates.

目次

第一章 緒論…………………………………………………………………....1
第一節 研究動機與目的…………………………………………………....1
第二節 論文架構…………………………………………………………....4

第二章 短期利率模型的介紹………………………………………………….5
第一節 連續時間短期利率模型………………………………………….....5
第二節 連續時間短期利率模型之實證估計……………………………….7
第三節 間斷時間利率模型之波動性
--GARCH、隨機波動性與狀態轉換模型…………………………10

第三章 短期利率模型樣本內估計之實證研究……………………………....13
第一節 研究動機與目的……………………………....................................13
第二節 實證模型與計量方法……………………………... ………………15
第三節 資料來源與基本統計量……………………………........................19
第四節 實證結果分析……………………………... ………………………21
第五節 結論……………………………... ……………………………........29

第四章 短期利率模型樣本外預測之實證研究……………………………...31
第一節 研究動機與目的……………………………...................................31
第二節 樣本外預測方法……………………………...................................32
第三節 資料來源與基本統計量…………………………….......................37
第四節 實證結果分析…………………………….......................................40
第五節 結論……………………………... …………………………….......49

第五章 短期利率隨機波動性之實證研究……………………………...........52
第一節 研究動機與目的……………………………...................................52
第二節 利率之波動性……………………………... ………………………54
第三節 資料來源與基本統計量……………………………........................61
第四節 實證結果分析……………………………... ………………………63
第五節 結論……………………………... ……………………………........71

第六章 結論............……………………………………………………………72

參考文獻……………………………... ……………………………...................74

圖表目次

表2-1 連續時間短期利率模型……………………………..................................... 5
表2-2 各短期利率模型下參數之限制……………………………......................... 6
表3-1 台灣商業本票收益率基本統計量……………………………....................21
表3-2 CKLS近似方法下之GMM與QML估計結果—月資料………………..22
表3-3 CKLS近似方法下之GMM與QML估計結果—週資料………………..23
表3-4 Nowman與CKLS近似下短期利率模型之QML估計結果—月資料…..25
表3-5 Nowman與CKLS近似下短期利率模型之QML估計結果—週資料…..26
表3-6 短期利率包涵模型之成對比較……………………………........................28
表4-1 台灣商業本票收益率基本統計……………………………........................39
表4-2 短期利率模型的估計與比較結果……………………………....................40
表4-3 短期利率包涵模型之成對比較……………………………........................41
表4-4 短期利率模型之成對比較--RMSE 比率…………………………….........44
表4-5 短期利率模型預測準確性與涵蓋訊息之成對比較—水準值預測………46
表4-6 短期利率模型預測準確性與涵蓋訊息之成對比較--波動性預測………..48
表5-1 短期利率及其一階自我廻歸殘差之基本統計量與診斷檢定…………….62
表5-2 條件平均數之參數估計結果…………………………….............................63
表5-3 CKLS模型之估計結果……………………………......................................64
表5-4 GARCH與GARCH-L模型下之估計結果…………………………….......65
表5-5 SV與SV-L模型之估計結果……………………………............................. 67
表5-6 MS與MS-L模型之估計結果……………………………........................... 68
表5-7 MS-SV與MS-SV-L模型之估計結果……………………………...............69
表5-8 水準模型的概似比檢定結果……………………………..............................70
圖3-1 台灣30天期商業本票初級市場周與月收益率及其變動趨勢圖…………..20
圖4-1　台灣30天期商業本票初級市場收益率趨勢圖……………………………..39
圖5-1 利率與其一階差分走势圖……………………………....................................61

參考文獻
林常青、洪茂蔚、管中閔，2002，台灣短期利率的動態行為：狀態轉換模型之應用，經濟論文，30卷第1期， 29-55.
葉仕國, 張美菁，2003，台灣貨幣市場短期利率模型的實證探討，交大管理學報， 23卷第1期， 37-57.
Ait-Sahalia, Yacine (1999), “Transition Densities for Interest Rate and Other Nonlinear Diffusions,” Journal of Finance, 54, 1361-1395.
Ait-Sahalia, Yacine (2002), “Maximum Likelihood Estimation of Discretely Sampled Diffusion: A Closed-form Approximation Approach,” Econometrica, 70, 223-262.
Bandi, F.M. and P. C. B. Phillips (2003), “Fully Nonparametric Estimation of Scalar Diffusion Models,” Econometrica, 71, 241-283.
Ball, C. A. and W. N. Torous (1999), “The Stochasitic Volatility of Short-Term Interest Rates: Some International Evidence,” Journal of Finance, 56, 2339-2359.
Bergstrom, A. R. (1983), “Gaussian Estimation of Structural Parameters in Higher-Order Continuous Time Dynamic Models,” Econometrica, 51, 117-152.
Bergstrom, A. R. (1984), Continuous Time Stochastic Models and Issues of Aggregation over Time (Handbook of Econometrics), 2, 1146-1210.
Bergstrom, A. R. (1985), “The Estimation of Parameters in Nonstationary Higher-Order Continuous Time Dynamic Models,” Econometric Theory, 1, 369-385.
Bergstrom, A. R. (1986), “The Estimation of Open Higher-Order Continuous Time Dynamic Models with Mixed Stock and Flow Data,” Econometric Theory, 2, 350-373.
Bergstrom, A. R.(1989), “Optimal forecasting of discrete stock and flow data generated by a higher-order continuous time system,” Econometric Theory, 2, 350-373.
Bergstrom, A. R. (1990). Continuous Time Econometric Modelling (Oxford: Oxford University Press)
Bollerslev, T. and Wooldridge, J.M. (1992), Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances, Econometric Reviews, 11, 143-172.
Brennan, M. J., and Schwartz, E. S. (1980), “Analyzing Convertible Bonds,” Journal of Financial and Quantitative Analysis, 15, 907-929.
Brenner, R. J., Harjes, R. H., and Kroner, K. F. (1996), “Another Look at Models of the Short-Term Interest Tate,” Journal of Financial and Quantitative Analysis, 31, 1, 85-107.
Broze, L., O. Scaillet, and J. Zakoian(1995), “Testing for Continuous Time Models of the Short-Term Interest Rate,” Journal of Empirical Finance, 2, 199-223.
Byers, S. L. and K. B. Nowman(1998), “Forecasting U.K. and U.S. Interest Rates Using Continuous Time Term Structure Models,” International Review of Financial Analysis, 7:3, 191-206.
Chan, K. C., Karolyi, G. A., Longstaff, F. A., and Sanders, A. B. (1992), “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate,” Journal of Finance, 47, 1209-1227.
Chen, L.(1996), “Stochastic Mean and Stochastic Volatility Three-Factor Model of the Term Structure of Interest Rates and Its Applications in Derivatives Pricing and Risk Management,” Financial Markets, Institutions and Instruments , 5, 1, 1-18.
Chong, Y. Y., and Hendry, D. F. (1986), “Econometric Evaluation of Linear Macro-Economic Models,” Review of Economic Studies, 53, 671-690.
Clements, M. P. and Hendry, D. F. (1993), “On the Limitations of Comparing Mean Square Forecast Errors,” Journal of Forecasting, 12, 617-637.
Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1980), “An Analysis of Variable Rate Loan Contracts,” Journal of Finance, 35, 389-403.
Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1985), “A Theory of the Term Structure of Interest Rates,” Econometrica, 53, 385-407.
Dahlquist, M. (1996), “On Alternative Interest Rate Processes,” Journal of Banking and Finance, 20, 1093-1119.
Diebold, F. X., and Mariano, R. S. (1995), “Comparing Predictive Accuracy,” Journal of Business and Economic Statistics, 13, 253-263.
Dothan, L. (1978), “On the Term Structure of Interest Rates”, Journal Financial Economics, 59-69.
Duffie, G.(1993), “On the Relation Between the Level and Volatility of Short-Term Interest Rates: A Comment on Chan, Karolyi, Longstaff and Sanders”, Working Paper of Federal Reserve Board, Washington D.C.
Duffie, D. and K.J. Singleton (1993), “Simulated Moments Estimation of Markov Models of Asset Prices,” Econometrica, 61, 929-952.
Eom, Y. H. (1998), “An Efficient GMM Estimation of Continuous-Time Asset Dynamics: Implications for the Term Structure of Interest Rates,” Working Paper, Yonsei University.
Episcopos, A. (2000), “Further Evidence on Alternative Continuous Time Models of the Short-term Interest Rate,” Journal of International Financial Markets, Institutions and Money, 10, 199-212.
Fair, R. and Shiller, R. (1990), “Comparing Information in Forecasts from Econometric Models,” Economic Review, 80, 375-389.
Florens-Zmirou, D.(1993), “On Estimating the Diffusion Coefficient from Discrete Observations,” Journal of Applied Probability, 30, 790-804.
Granger, C. W. J. and Newbold, P., (1973), “Some Comments on the Evaluation of Economic Forecasts,” Applied Economics, 5, 35-47.
Granger, C. W. J. and Newbold, P., (1986), Forecasting Economic Time Series (2nd ed.) Orlando, FL: Acadamic Press.
Gray, S. F. (1996), “Modelling the Conditional Distribution of Interest Rates as a Regime-Switching Process," Journal of Financial Economics, 42, 27-62.
Hamilton, J. D. (1989), “A New Approach to the Economics Analysis of Non-Stationary Time Series and the Business Cycle,” Econometrica, 57, 357-384.
Hansen, L. P. (1982), “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, 50, 1029-1054.
Hansen, B. E. (1996), ”Erratum: The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP,” Journal of Applied Econometrics, 11(2), 195-98.
Harvey, D. I., Leybourne, S. J., and Newbold, P. (1998), “Tests for Forecast Encompassing,” Journal of Business and Economic Statistics, 16, 254-259.
Harvey, A., Ruiz, E. and N. Shephard (1994), “Multivariate Stochastic Variance Models,” Review of Economic Studies, 61, 247-264.
Hong, Y., H. Li, and F. Zhao(2002), “Out-of-Sample Performance of Spot Interest Rate Models,” working paper.
Lo, Andrew W (1988), “Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data,” Econometric Theory, 4, 231–247.
Longstaff, Francis, and Eduardo Schwartz(1992), “Interest Rate Volatility and the Term Structure: A Two- Factor General Equilibrium Model,” Journal of Finace, 47, 1259-1282
Merton, R. (1973), “Rational Theory of Option Pricing,” Bell Journal of Economics and Management Science, 4, 141-183.
Newey, W. K. and West, K. D. (1994), “Automatic Lag Selection in Covariance Matrix Estimation,” Review of Economic Studies, 61, 631-653.
Nowman, K. B. (1997), “Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates,” Journal of Finance, 5, 1695-1706.
Nowman, K. B. (1998), “Continuous-Time Short Term Interest Rate Models,” Applied Financial Economics, 8, 401-407.
Nowman, K. B. (2002), “The Volatility of Japanese Interest Rates Evidence for Certificate of Deposit and Gensaki Rates, 11, 29-38.
Nowman, K. B. and B. Saitoglu(2003), “Continuous Time and Nonparametric Modelling of U.S. Interest Rate Models,” International Review of Financial Analysis, 12, 25-34.
Pagan, A. and Schwert, G., (1990), “Alternative Models for Conditional Stock Volatility,” Journal of Econometrics, 45, 267- 290.
Sandman, G. and Koopman, S. (1998), Estimation of stochastic volatility models via Monte Carlo maximum likelihood, Journal of Econometrics, 67, 271-301.
Smith D. R. (2002), “Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates,” Journal of Business and Economic Statistics, 20, 183-197.
Treepongkaruna, S. and Gray, S.(2003), “On the Robustness of Short-term Interest Rate Models,” Accounting and Finance, 43, 87- 121.
Vasicek, O. A. (1977), “An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics, 5, 177-188.
Vuong, Q. H. (1989), “Likelihood Ratio Test for Model Selection and Non-Nested Hypotheses,” Econometrica, 57, 307-333.
West, K. and Cho D., (1995), “The Predictive Ability of Several Models of Exchange Rate Volatility,” Journal of Econometrics, 69, 367-3