最大平滑度遠期利率曲線配適模型之再探討

Further Study on Fitting Forward Rate Curves with Maximum Smoothness

李賢源(Shyan-Yuan Lee) ； 林慧貞(Huey-Jen Lin)

《中國財務學刊》 6卷1期 (1998/07) Pp. 45-75

https://doi.org/10.6545/JoFS.1998.6(1).2

摘要

最大平滑度遠期利率曲線配適模型，係指以最大平滑度為目標函數、債券價格為限制條件求解遠期利率函數之方法，以Adams and Deventer（1994）為代表。本文第一部份旨在對此配適方法之理論性質做進一步之探討，指出原模型在求解上之問題、及其參數估計值對條件式之選取具相當敏感之性質，進而分析該模型適用之樣本型態，並提出另一種找尋適當條件式之方法，以擴大此模型之適用範圍；此外，亦將Adams and Deventer模型作不同角度之擴展，如修改最大平滑度之定義、以附息債券資料取代原模型採用之零息債券資料、及最適之遠期利率函數可否為多項式以外之函數型態等探討；最後並將此種配適方法應用於配適一條平滑之殖利率曲線。本文第二部份則對Adams and Deventer模型進行實證研究，分別利用票券、臺幣利率交換、及政府債券資料配適遠期利率曲線，並以利率交換資料配適殖利率曲線。

關鍵字

存續期限調整法 ； 最大平滑度 ； 殖利率曲線 ； 逐步嵌入估計法 ； 遠期利率曲線 ； 零息債券調整法

並列摘要

Adams and Deventer (1994) showed a model for fitting forward rate curves which are solved by using the maximum smoothness as the objective function and the observed bond prices as the constrained conditions. The first part of this paper provides further study on the theoretical essence of Adams and Deventer's model. We find that the parameters of the forward rate function are very sensitive to the constrained conditions and not all of the samples are suited for the conditions suggested by Adams and Deventer. As for these samples, an approach for finding advisable conditions is introduced in this paper. In order to test if the original specifications are the best. some revisions are tried. such as changing the definition of maximum smoothness, using coupon bond data instead of zero-co upon bond data, and trying the possibility of other forward rate functional forms. Furthermore, this model is extended to the application of fittingyield curves. The second part is made up of empirical studies. Adams and Deventer's model is applied to fit the forward rate curves by using the short-term bill. interest rate swaps, and government bond data in the Taiwan market: the interest rate swap data is also used to fit the yield curves in the way derived in this paper.

並列關鍵字

duration adjustment method ； forward rate curves ； maximum smoothness ； spline method ； yield curves ； zero-coupon adjustment method