在現代資產定價的研究中，短期利率扮演一個很重要的角色。短期利率模型中最重要的一類是連續時間的擴散模型(continuous-time diffusion model)。這些模型有一個特性：假設已知利率的動態過程，亦即對利率模型的漂移項及擴散項作特定函數型態假設，而並無完整的經濟理論說明為何如此設定。我們知道不同的利率模型設定會推導出不同的商品評價公式，因此任意函數型態的模型一旦設定偏誤太大，勢必對評價公式的準確性造成很大的影響。有鑑於此，近幾年來利用無母數統計方法來估計利率模型的文獻與日具增。因為利用無母數統計方法可以減少對利率模型的任意設定。

基於對短期利率模型任意參數設定的懷疑，以及欲探究台灣短期利率的動態過程究竟為何種型態，因此本文以Stanton(1997)的無母數統計法利率模型，以台灣貨幣市場30天期的商業本票利率資料作實證分析。而為了更清楚了解無母數法利率模型的表現，本文亦採用CKLS (1992)所發展的估計方法，以一般化動差法(Generalized method of moment, GMM)估計九個有參數利率模型，將所得到結果與無母數法的利率模型比較。最後，我們利用估計出的無母數利率模型來建構利率期間結構，並與實際資料作比較。

本文實證結果發現，台灣短期利率的動態過程不管是漂移項或擴散項函數皆呈現非線性型態，且漂移項函數呈現負斜率的均數回歸(mean reverting)現象，而擴散項函數大致是隨利率水準愈大而其數值亦愈大。因此若以非線性、具有均數回歸且擴散項是遞增的函數式來設定利率模型的參數，應該較能刻劃台灣短期利率動態過程。另外，從有參數模型的實證結果發現，漂移項或擴散項函數，只要其中一項設定有誤，不僅會使該項的預測能力變差，亦連帶會影響另一項的預測能力，進而也會影響模型的整體表現。這意味著以無母數方法來估計利率模型有其必要性。最後，我們利用無母數法利率模型所估計的利率期間結構與實際的資料比較，發現估計結果還算不錯。

【中文部分】

[1] 林炳輝、葉仕國，台灣金融市場跳躍—擴散利率模型之實證研究，Journal of Financial Studies Vol.6 No.1, July 1998, pp. 77-106。

[2] 林長青、洪茂蔚、管中閔，台灣短期利率的動態行為：狀態轉換模型的應用，
經濟論文，30：1, 2002, pp. 29-55。

[3] 中央銀行年報，民國79年至民國91年。

[4] 葉仕國，整合性利率期限結構模型之實證研究，民國86年。

【英文部分】

[1] Aït-Sahalia, Yacine, “Nonparametric Pricing of Interest Rate Derivative Securities”, Econometrica, May 1996a, Vol. 64. No. 3, pp. 527-560.
[2] Aït-Sahalia, Yacine, “Testing Continuous-Time Models of the Spot Interest Rate”, The Review of Financial Studies, Spring 1996b, Vol 9, No. 2, pp. 385-426.

[3] Backus, David K., Silverio Foresi, and Stanley E. Zin, “Arbitrage opportunities in arbitrage-free models of bond pricing”, working paper, 1995, New York University.

[4] Bandi, Federico M., Thong H. Nguyen, “On The Functional Estimation of Jump Diffusion Models”, working paper, February 5, 2001.

[5] Boudoukh, Jacob, Matthew Richardson, Richard Stanton and Robert F. Whitelaw,
“A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate Volatility”, working paper, June 17, 1999.

[6] Chan, K. C., G. Andrew Karolyi, Francis A. Longstaff, and Anthony B. Sanders, “An Empirical Comparison of Alternative Models of The Short-Term Interest Rate”, The Journal of Finance, July 1992, Vol. XLVII. No. 3, pp. 1209-1227.

[7] Conley, T., L. Hansen, E. Luttmer and J. Scheinkman, “Short-Term Interest Rates as Subordinated Diffusions”, Review of Financial Studies 10, 1997, pp. 525-577.

[8] Cox, John C., Jonathan E. Ingersoll, Jr., and Stephen A. Ross, “A Re-examination of Traditional Hypotheses about The Term Structure of Interest Rates”, Journal of Finance 36, 1981, pp. 769-799.

[9] Cox, John C., Jonathan E. Ingersoll, Jr., and Stephen A. Ross, “A Theory of The Term Structure of Interest Rates”, Econometrica 53, 1985, pp. 385-467.

[10] Epanechnikov, V. A., “Nonparametric estimates of multivariate probability density”, Theory of Probability and Applications 14, 1969, pp. 153-158.

[11] Fabozzi, Frank J, “Interest rate, term structure, and valuation modeling”, Hoboken, N.J. : Wiley, c2002.

[12] Fama, Eugene F., “Term Premiums in Bond Returns”, Journal of Financial Economics 13, 1984, pp. 529-546.

[13] Greene, William H., “Econometric Analysis”, New Jersey: Prentice Hall, Inc., 2000, 4th edition.

[14] Hansen, Lars Peter, “Large sample properties of generalized method of moments estimators”, Econometrica 50, 1982, pp.1029-1054.

[15] Hansen, Lars Peter, and Jose` A. Scheinkman, “Back to the future: Generating moment implications for continuous-time Markov process”, Econometrica 63, 1995, pp.767-804.

[16] Hong, Yongmiao, Haitao Li and Feng Zhao, “Out-of-Sample Performance of Spot Interest Rate Models”, working paper, March 2002.

[17] Johannes M., “Jump in Interest Rates: A Nonparametric approach”, working paper, 2000.

[18] Krylov, N.V., “Introduction to the Theory of Random Process”, Rhode Island: American Mathematical Society”, 2002.

[19] Künsch, H. R., “The Jackknife and The Bootstrap for General Stationary Observations”, Annals of Statistics 17, 1989, pp. 1217-1241.

[20] Lamoureux, Christopher G. and H. Douglas Witte, “Empirical Analysis of the Yield Curve: The Information in the Data Viewed through the Window of Cox, Ingersoll, and Ross”, The Journal of Finance, June 2002, Vol. LVII. No. 3, pp. 1479-1519.

[21] Litterman, R., and J. A. Scheinkman, "Common Factors Affecting Bond Returns." Journal of Fixed Income 1, 1991.

[22] Lo, Andrew W., and Jiang Wang, “Implementing option pricing models when asset returns are predictable”, Jouranl of Finance 50, 1995, pp.87-129.

[23] Longstaff, Francis A. and Eduardo S. Schwartz, “Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model”, The Journal of Finance, September 1992, Vol. XLVII. No. 4, pp. 1259-1282.

[24] Pagan, A., and Aman Ullah, ‘Nonparametric Econometrics”, New York: Cambridge University Press, 1999.

[25] Pfann, Gerard A., Peter C. Schotman, and Rolf Tschernig, “Nonlinear Interest Rate Dynamics and Implications for The Term Structure”, Journal of Econometrics 74, 1996, pp. 149-176.

[26] Pritsker, M., “Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models”, The Review of Financial Studies, Fall 1998, Vol 11, No. 3, pp. 449-487.

[27] Scott, David W., “Multivariate Density Estimation: Theory, Practice and Visualization”, John Wiley, New York, 1992.

[28] Stanton, R., “A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk”, The Jouranl of Finance, December 1997, Vol. LII, No 5, pp. 1973-2002.

[29] Vasicek, Oldrich, “An Equilibrium Characterization of The Term Structure”, Journal of Financial Economics 5, 1997, pp. 177-188.