臺灣博碩士論文加值系統

固定資產的分析，從債券的交易到衍生性金融商品的評價，都需從利率期限結構的建構開始。對於利用何種方法去估計利率期限結構仍有爭議。例如從選擇何種固定資產作為評價的樣本、配適的標的為何(折現、即期、遠期利率函數)等。在實務上，以實際資料所繪製的實證利率期限結構仍為普遍採用的模式。而建構實證利率期限結構必須兼顧平滑度及精確度兩個目標。本文主要的目的是依據Pham (1998)首次使用的契比雪夫多項式模型，去配適台灣公債的利率期限結構。並選用國內Lin (1999)以樣條函數為基礎來測繪我國的收益曲線的文章作比較。並利用櫃檯買賣中心的成交價報價和Lin (1999)的選樣資料、兩種參數設定(四個參數、六個參數)，去做對於配適利率期限結構不同變數結果可能造成的影響。實證結果如下：
一、契比雪夫多項式被工程和科學界所善用，而本論文卻是第一次將他使用在配適台灣公債的利率期限結構。
二、Chebyshev polynomials配適的殖利率曲線可克服部分傳統使用spline 和回歸(regression)方法配適時所產生的弱點。模型克服部分因為要求曲線平滑而設定了不同程度的限制。Chebyshev polynomials不要求特別的函數形式，卻可得到平滑的殖利率曲線。此外，。Chebyshev polynomials模型可適用於各種資料的配適。
三、在四種情形下，契比雪夫多項式所配適出的利率期限結構(即期利率曲線、遠期利率曲線)，皆相當的平滑。而得出的即期利率曲線相當的穩定且符合市場上的狀況。但遠期利率曲線在長期時，會產生負值和利率超過1等不合理的情形。

Fixed-income analysis, from bond trading to derivatives valuation, are based on the term structure of interest rates. Issues arise as to the methodology for estimating a tem structure, such as which fixed —income prices to be used as inputs, which curves to be estimated (forward, spot, or discount function). The Objectives in empirical estimation of the term structure are smoothness and accuracy. The purpose of this thesis is to fit the term structure of interest rates for Taiwanese government bonds by using the Chebyshev polynomials model which was first used by Pham (1998). And results are compared with the paper published by Lin (1999), which applies the spline function techniques to fit the yield curve in Taiwanese government bonds.
The contribution and conclusion of this study are as follows：
1. While Chebyshev polynomials are well known in engineering and science, this thesis is the first to use it to fit the term structure of interest rates in Taiwanese government bonds.
2. Chebyshev polynomials possess desirable properties that improve the econometrics of zero-coupon yield curve fitting. Specifically it can partly overcome the problem of arbitrary degree of smoothing in that it does not require specification of a functional form. Moreover, Chebyshev polynomials makes use of the entire range of available date.
3. In four conditions，we can get smoothness to fit the term structure of interest rates by using the Chebyshev polynomials model. The spot rate curve look stabl and reliable. However, the forward rate curve fluctuate more dramatically for longer maturity and decline to negative values for longer maturity.

第一章 緒論1
第一節 研究動機1
第二節 研究目的3
第三節 研究架構5
第二章 文獻探討6
第一節 文獻回顧6
第二節 利率期限結構之均衡模式9
第三節 利率期限結構估計之實證近似模式12
第四節 實證研究：國際性的觀點21
一、利率期限結構的國外實證論文回顧：22
二、利率期限結構的國內實證論文回顧：24
第三章 研究設計與方法27
第一節 研究假設27
第二節 研究資料說明27
第三節 模型介紹29
一、估計利率期限結構一般式29
二、Chebyshev polynomials模型再探討31
第四節 實證統計分析38
一、準確度比較的準則38
二、平滑度的衡量38
第五節 研究限制39
一、債券樣本的選取39
二、在模型參數的限制上39
三、忽略交易成本和賦稅39
第四章 實證結果41
第一節 資料輸入與說明41
第二節 契比雪夫模型的實證結果42
一、模型的配適度42
二、平滑度50
三、模型配適出的即期利率和遠期利率52
四、因素分析59
第五章 結論與建議61
第一節 實證結論61
一、利率累加函數(interest cumulator)61
二、模型的配適力61
三、平滑度63
四、利率期限結構63
第二節 建議64
一、模型特質的探討64
二、參數的選取65
三、樣本的選取65
四、模型的預測性66
參考文獻67
附錄一 本研究所選取的公債樣本資料72
附錄二 利用契比雪夫折現配適模型所估出的參數76
附錄三 利用契比雪夫折現配適模型所估出的參數(續)83

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