臺灣博碩士論文加值系統

　　本文主要探討曲線配適方法與無套利評價模型間之一致性對於利率衍生性商品評價的重要性。以指數內插法、Nelson and Siegel (1987)及Steeley (1991)三種曲線配適方法，與Heath, Jarrow and Morton (1992)及Hull and White (1994)兩種利率模型，交互進行組合配對（包含具一致性及不具一致性之組合），針對公債期貨評價，得到六種不同的評價結果。研究重點為：1.利用曲線配適方法建構平滑的利率期限結構，2.將配適結果輸入利率模型中，作為初始的殖利率曲線 (initial curve)，進而評價公債期貨；與實際交易價格比較，選出六種評價結果中，價格誤差較小者，即求得最佳曲線配適方法與利率模型之組合。研究結果顯示，選擇與利率模型間具有一致性的曲線配適方法，除了可降低參數估計的不穩定性之外，評價誤差也較低；本研究求得最佳配適方法與利率模型之組合為Nelson and Siegel (1987)與Hull and White (1994)，在樣本期間內，對公債期貨評價的平均誤差為0.0379。

This study investigates the importance of consistence with fitting curve techniques and arbitrage free interest rate model for pricing interest derivatives. We employ three different yield curve fitting methods which are exponential interpolation method, Nelson-Siegel (1987) and Steeley (1991) and use them as input to estimate the parameters for two different interest rate models, Heath-Jarrow-Morton (1992) and Hull-White (1994), to pricing Taiwan Treasury bond futures. The results show that the combination of consistent fitting curve method and interest rate model helps in stabilizing the parameters estimators and reducing the pricing error of bond futures. We present the best combination of fitting curve method and interest rate model is Nelson-Siegel method and Hull-White model with the mean percentage error of bond futures 0.0379.

第一章 緒論
第一節　研究動機與研究目的..............................1
第二節　研究架構........................................4
第二章　曲線配適方法及利率模型之文獻回顧
第一節　利率期限結構配適方法文獻回顧....................7
第二節　利率模型文獻回顧...............................10
第三節　期限結構一致性模型與利率衍生性商品評價.........13
第三章　一致性模型與公債期貨評價之研究方法...............15
第一節　配適初始利率期限結構...........................16
第二節　公債期貨之評價方法.............................19
第四章　實證結果分析
第一節　資料來源.......................................25
第二節 台灣公債市場利率期限結構之估計
一、　三種曲線配適方法結果分析......................27
二、　不同方法之配適能力比較........................35
第三節 公債期貨之評價
一、　HJM模型配合三種曲線配適方法之評價.............37
二、　Hull-White模型配合三種曲線配適方法之評價......41
第四節 評價誤差比較結果................................45
第五章　結論與建議
第一節　研究結論.......................................46
第二節　後續研究建議...................................48
參考文獻.................................................49

圖目錄

【圖1】一致性利率模型架構圖...............................5
【圖2】研究流程圖.........................................6
【圖3】Hull and White三元樹利率走勢圖....................22
【圖4】指數內插法求解即期利率圖..........................28
【圖5】指數內插法建構之即期利率期限結構..................29
【圖6】指數內插法建構之遠期利率期限結構..................29
【圖7】Nelson and Siegel模型建構之即期利率期限結構.......31
【圖8】Nelson and Siegel模型建構之遠期利率期限結構.......32
【圖9】Basis-spline曲線模型建構之即期利率期限結構........34
【圖10】Basis-spline曲線模型建構之遠期利率期限結構.......34
【圖11】公債期貨價格計算過程圖...........................38
【圖12】HJM模型評價公債期貨過程圖........................40
【圖13】Hull and White利率三元樹.........................42
【圖14】Hull and White模型評價公債期貨過程圖.............43

表目錄

【表1】各種曲線配適方法之文獻回顧.........................9
【表2】一般均衡利率模型之文獻回顧........................11
【表3】無套利機會利率模型之文獻回顧......................12
【表4】十年期公債契約規格................................25
【表5】指數內插法配適結果................................28
【表6】Nelson and Siegel模型配適結果.....................31
【表7】Basis-spline曲線配適結果......................... 33
【表8】三種方法配適能力比較..............................36
【表9】HJM模型配合三種曲線配適方法參數估計結果...........41
【表10】HJM模型配合三種曲線配適方法評價誤差..............41
【表11】Hull and White模型配合三種曲線配適方法參數估計結果44
【表12】Hull and White模型配合三種曲線配適方法評價誤差...44
【表13】六種評價結果誤差比較.............................45

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