狀態變化下的利率模型估計：門檻方法之應用

Abstract

依循資產定價理論推導得出之利率模型具有“無套利'之經 濟意義，但在做模型設定檢定時大多被拒絕。2002 年，邦索和周 提出了一個馬可夫轉態利率模型，不但通過了模型設定檢定，其 統計性質亦令人相信與真實資料相當接近。不過，它假設下期系 統狀態無法由本期擁有的資訊決定，因此這個模型無法利用本期 資訊預測下期利率。 針對上述這個缺點，本論文嘗試用門檻函數來決定系統狀態 之轉態利率模型，文獻中尚未發現有人做過類似的工作。我們並 使用此類模型中最簡單的一個設定，以及真實利率資料來做估 計。為了完成這個模型的估計，相較於標準的效率動差法，我們 必須更動其中一些步驟。在這些更動之後，估計值收斂的速度在 半小時以內。雖然這個簡單的設定表現不夠好，但在本論文研究 過程中發展的程式及累積的經驗，將可做為未來繼續研究此類模 型的最佳工具。

Interest rate models abiding by the martingale pricing theory are economically meaningful, but usually strongly rejected by specification tests. Recently, a regime switching model proposed by Bansal and Zhou (2002) was found to match the statistical properties of yield curves very well, but it assumed that regimes are unobservable such that the yield of next period is un-predictable from the present information. This study is a first attempt to propose a family of models with regime shift controlled by a threshold function, which is also derived from the martingale pricing theory. The family of models could be used to predict the regime and the yield of the next period from the present information. Among them, one simple threshold model with the threshold function a linear form of the realized pricing kernel value and two threshold parameters is used to fit six month and five year yields by Efficient Method of Moment (EMM). Along with some reasonable modifications on the standard EMM procedures, the estimation could be done within half an hour on PCs with 1.7GHz CPU. The computer programs developed during this study may serve as a useful tool for future investigation on this family of threshold models.