Fitting the Term Structure of Interest Rates in Taiwan Government Bonds Market

[[abstract]]本研究主要目的在比較Exponential B-spline 模型、Diament 模型和Mansi and Phillips 模型對台灣公債市場利率期限結構的配適能力優劣。相較於國外債券市場，台灣公債市場的流動性較差，因此在建構利率期限結構時必須特別考量此一限制。 由於國內以 B-spline函數為基礎估計利率期限結構時，對於參數及節點的設定，未依債券到期日實際情形分段配適，故本研究為配合參數設定的實際意義，將Exponential B-spline 模型的樣本期間分成三個階段進行估算，分別設定不同的節點位置，以求獲得更精確的估算結果。Diament 所提出的模型可獲得平滑的殖利率曲線，且模型中的參數皆有經濟意義。由於Diament模型必須先知道殖利率形狀才能應用適合的模型估計利率期限結構，否則會有無法收斂的情形，因此Mansi and Phillips改善Diament模型的缺點，提出可以捕捉不同形狀殖利率曲線的模型。 經實證後發現：(一) 使用分段配適的確能有效提高Exponential B-spline模型的配適能力。(二) 在考慮流動性不足限制下，所有模型的配適能力均優於未考慮流動性不足之效果。(三) 不論是否考慮流動性不足的情況下，皆以Exponential B-spline 模型的配適度最佳。[[abstract]]This paper is to compare Exponential B-spline model、Mansi and Phillips model and Diament model about their term structure of interest rate fitting performances in Taiwan Government Bonds (TGB) market. Compared with foreign bond markets, the TGB market is an illiquid bond market with fewer trading volume; therefore, we must include the illiquidity constraint when estimating the term structure of interest rate in TGB market. The previous empirical studies have applied the B-spline function in estimating the TGB term structure without considering different maturity of bond and specifying the appropriate parameters and knots. For the real phenomena of setting parameters, this paper divides the sample periods into three sub-periods and separately specifies different time horizon and knot values to get more precise fitting performance. The major advantage of Diament model is that it could obtain a smooth yield curve. Besides, the parameters of Diament model have different economic meaning. A disadvantage of the Diament model is that the user must first observe the yield curve to decide whether the monotonic or the non-monotonic form applies , otherwise there is a convergent problem. Hence, Mansi and Phillips modify and improve the Diament approach. Their model can describe different shape of term structure of interest rate. The empirical results are: (1) Considering different maturity of bond and specifying the appropriate parameters and knots can raise the fitting performance of Exponential B-spline model. (2) After taking illiquidity constraint into account, all models will have better fitting performance than not take illiquidity constraint into consideration. (3) In terms of fitting performance, the Exponential B-spline model is the best