| Abstract: | 我國中央政府公債(簡稱公債)之發行,隨著政府推動國家六年建設計畫而逐年增加,使得我國的中央政府公債市場逐漸發展成長短期債券並存的局面,而公債市場的利率問題便成為重要的研究課題。研究公債市場利率問題首先就是要對此一市場中同時存在的各種天期債券間之利率(或價格)關係有所了解。在早期,利率期限結構之產生是將各個債券之到期收益率以簡單的目視法平滑地連結而成,但此法的缺點是缺乏一致性。McCulloch(1971,1975, 1976)則改以二次樣條將各種天期債券間之利率關係以迴歸方式求出。為避免二次樣條在各連結點的二次微分不連續而使得利率結構中所隱含的遠期利率結構有轉折點而不夠平滑,本研究因此改採指數多項式迴歸、三次樣條迴歸、指數三次樣條迴歸、以及基底樣條迴歸等四種方式估計我國政府公債的利率期限結構,探討用不同的方法所估計出我國公債利率期限結構之優劣,並建立資料庫以供日後研究各種有關我國的利率問題時使用。在這四種估計方法中,指數多項式雖然理論上較傳統多項式估計貼現函數應有較好的結果,但相對於其他三種估計方法則顯示較不穩定,因此指數多項式的估計方法可以不用考慮。若以均方差作為選擇估計方法的標準,則一般仍以McCulloch的立方樣條的估計較為適合,但若時間與人力允許,則立方樣條與基底樣條可以同時估計後,再選取均方差較小的。不過,無論以何種方法估計我國公債市場的利率期限結構,結果都顯示十年以上長天期的利率有上漲的現象,而造成遠期利率急速上揚。在未明白為何我國公債市場長天期利率經常持續上揚之際,我們應該採取較保守的態度,而只接受十年期以下的估計值。
The issuance of central government`s bonds has been increased with the National Six Year Development Plan. Both long-term and short-term government bonds have been actively traded on our government bond market. It is important to study first the term structure of interest rates of government bonds before proposing to study other related interest rate issues of our government bonds. In early days, the method of eyeball fitting yield-to-maturity of various government bonds was the major way to construct the term structure of interest rates. Such a method oftentimes created an inconsistent result. McCulloch (1971, 1975, 1976) proposed to use the quadratic spline regression to estimate the term structure of interest rates. To avoid the problems of discontinuity of forward rates at various nodes, this research instead using exponential polynomial, cubic spline, exponential cubic spline, and basis spline regression to estimate the term structure of interest rates of our government bonds. We investigate which method is the best for such a work. According to our estimates, we also establish a data base of our government bond`s term structure of interest rates. Among these four estimation methods, we find that exponential polynomial can be excluded. According to the mean-square-error (MSE) criterion, the cubic spline regression usually has the best result. If time and resources are not problems, both cubic spline and basis spline regressions may be used, and then select the one with the least MSE. Regardless which method is adopted to estimate the term structure of interest rates, however, all results indicate that the interest rates over ten years are usually rising. Such a phenomenon makes the corresponding forward rates also rise sharply. Before knowing the reasons why exists such a phenomenon, it is wise to use only those in-sample estimates of interest rates with maturity less than ten years. |
