以分段三次方指數函數配適台灣公債市場之利率期限結構：線性最適化與非線性最適化之比較

Fitting the Term Structure of Taiwan Government Bond Market with Cubic Exponential Spline Function: A Comparison between Linear Optimization Method and Nonlinear Optimization Method

10.6545/JoFS.2000.8(2).2

謝承熹(Cheng-His Hsieh)

利率期限結構 ； 殖利率曲線 ； 折現因子 ； 分段三次方指數函數 ； Term Structure of Interest Rates ； Yield Curve ； Discount Factor ； Cubic Exponential Spline

中國財務學刊

8卷2期（2000 / 08 / 31）

25 - 47

繁體中文

本文以分段三次方指數函數（Cubic Exponential Spline Fitting）配適95/6/21至99/12/29臺灣公債市場每週三的利率期限姞構。首先，文中假設折現因子具分段三次方指數函數形式，接著分別以線性最適化與非線性最適化法估計參數，求得折現函數，並轉換而得利率期限結構。在資料期間內，本文發現線性最適化法的估計誤差較非線性最適化法小，且估計所需時間亦較短；因此，在降低估計誤差和估計時間的考量下，本文建議在配適利率期限結構時，應以線性適化法來配適較為適當。

This study is designed to fit the term structure of Taiwan government bond market by applying the cubic exponential spline method on ev.ery Wednesdays from 1995/6/2 1 to 1999/12/29. It is presumed in the study that the functional form of discount factor is a cubic exponential spline function. Since the estimated parameters are used to calculate the discount function for each period, the term structure of interest rates can then be obtained through the discount function. In this sense, the linear and nonlinear optimization methods are employed respectively to estimate parameters embedded in the discount function. The result of this study shows that, with the application of linear optimization method, the fitting errors is smaller and fitting time is shorter than those estimated by nonlinear optimization method Therefore, with the concern of reducing the fitting error and the fitting time, the linear optimization approach is a better fitting method than nonlinear optimization method.

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