臺灣博碩士論文加值系統

本文進行數值分析面的利率模型比較，包括Black-Derman-Toy的二元利率樹與Hull-White的三元利率樹。本研究的數值檢定涵蓋三個主題：第一，本研究檢定Black-Derman-Toy、Hull-White模型期初期間結構的密合程度。第二，利用市場資料，使用Black-Derman-Toy、Hull-White模型，比較未來短期利率的預測能力。第三，比較Black-Derman-Toy、Hull-White模型，在利率選擇權評價上的精確度。同時，本文利用不一樣的分割期數對Black-Derman-Toy、Hull-White利率模型進行分析面的比較。本研究以央行發行公債的利率期間結構為樣本資料，分別以Matlab Financial Toolbox(1999)公司債附屬賣權評價的案例，及Hull-White(1996)德國1994年7月8日的利率期間結構測試利率選擇權。本研究的執行與程式皆在Matlab語言上進行。本研究獲得以下幾個結論：第一，Black-Derman-Toy、Hull-White模型，在利率樹期間結構的密合程度皆相當優良，誤差率在5%以下。第二，對未來利率的預測在二年內有效，但隨著外插期間愈長，偏誤率愈大。第三，Black-Derman-Toy、Hull-White模型，在計算利率選擇權皆有良好的精確度。第四， Hull-White三元利率樹所切割的期間愈細，表現的數值收斂性愈好，而Black-Derman-Toy二元利率樹則沒有任何顯著改善。

This thesis empirically compares computational aspects of term structure models, including binomial interest rate tree of Black-Derman-Toy''s and trinomial interest rate tree of Hull-White''s. The numerical tests of this study cover three topics. First, this study tests the precision of implementation of initial term structures of Black-Derman-Toy and Hull-White. Second, by using market data this study compares the forecasting efficacy of future short rates between Black-Derman-Toy and Hull-White. Finally, this research conducts a comparison of computational accuracy of Black-Derman-Toy and Hull-White in pricing of interest rate derivatives. Meanwhile, all three experiments of the above are executed repeatedly in different time steps of lattice structures to test numerical improvements of Black-Derman-Toy and Hull-White. This thesis uses Taiwan fixed-income security market data (1992-1993) for the purposes of the first and second tests. Data of Matlab''s Financial Toolbox (1999) and Hull-White(1996) are used in the testing of interest rate derivatives. All the experiments are executed and programmed by Matlab language. This study draws the following preliminary conclusions. First, both Black-Derman-Toy and Hull-White show good match of the initial term structure of market by a deviation rate less than 5%. Second, future rate forecasts are only possible within two years and deteriorate with the increasing of forecasting time horizon. Third, both Black-Derman-Toy and Hull-White have reasonable accuracy in pricing the interest rate options. Finally, Hull-White trinomial tree shows good numerical convergence when the lattice structure getting finer while Black-Derman-Toy has not any significant improvements.

目錄
目錄 頁次
中文摘要……………………………………………………………...…. Ⅰ
英文摘要………………………………………………………….…….….Ⅱ
誌謝…………………………………………………………………….....Ⅳ
目錄………………………………………………………………………...Ⅴ
表目錄…………………………………..…….………………………..…Ⅵ
圖目錄………………………………..……………….…………………..Ⅷ
第壹章 緒論…………………………..………………….…..………….1
第一節 研究動機…………………..…………………….…………….1
第二節 研究目的…………………...………………………....…….2
第三節 研究範圍…………………………………………..………..…3
第四節 研究流程…………………………………………..…………..4
第貳章 文獻探討…………………..………………………..………..…6
第一節 均衡模型…………..………………….………..………….…6
第二節 無套利模型………………………….………..…………..…11
第參章 研究方法………………………..……………..….……………17
第一節 Hull & White三元樹模型…..……………..…...………..17
第二節 Black, Derman and Toy二元樹模型…………..…..………21
第三節 Hull-White與Black-Derman-Toy模型之比較….……………28
第四節 研究設計………………………………………..…………….30
第肆章 實證結果與分析………..………………………..…..……….34
第一節 利率期間結構的密合程度……………………..………….…34
第二節 利率選擇權定價的正確程度……………………..………….39
第伍章 結論與建議………………..…………..……….……..……..41
參考文獻…………………………………………...….…..……….….43
附錄………………………………………..………..……..……….….47
表目錄
表1：利率模型比較………………………………………….……….….14
表2：H-W與BDT模型參數比較表……………………….…………......28
表3：12個時點的債券市場利率期間結構……………..…………….…31
表4：12個時點之未來短期利率………………………………………….31
表5：利率期間結構例子…………………………………….…………..32
表6：德國1994年7月8日的利率期間結構……………….………....…32
表7-1：BDT期初結構密合偏誤(%)…………………….………….….…35
表7-2：BDT未來短期利率預測偏誤(%)…………….….…………….…35
表7-3：H-W期初結構密合偏誤(%)…………………….……………..…35
表7-4：H-W未來短期利率預測偏誤(%)……………….…………….….36
表8-1：BDT期初結構密合偏誤(%)……………………….…………..…36
表8-2：BDT未來短期利率預測偏誤(%)………………………………...37
表8-3：H-W期初結構密合偏誤(%)………………………..………….…37
表8-4：H-W未來短期利率預測偏誤(%)…………………..………….…37
表9：BDT求解利率選擇權的精確度…………..…………….………...39
表10：H-W求解利率選擇權的精確度……………..………..………….40
附表1-1：BDT期初結構密合偏誤(%)……………….……………….….47
附表1-2：BDT未來短期利率預測偏誤(%)……….….…………….…..47
附表1-3：H-W期初結構密合偏誤(%)………………………………...…47
附表1-4：H-W未來短期利率預測偏誤(%)………………………….…..48
附表2-1：BDT期初結構密合偏誤(%)…………………..…………….…48
附表2-2：BDT未來短期利率預測偏誤(%)……………………………...48
附表2-3：H-W期初結構密合偏誤(%)…………………..…………….…49
附表2-4：H-W未來短期利率預測偏誤(%)……………..…………….…49
附表3-1：BDT期初結構密合偏誤(%)……………….…………………..49
附表3-2：BDT未來短期利率預測偏誤(%)……….….………………….50
附表3-3：H-W期初結構密合偏誤(%)…………………..…………..….50
附表3-4：H-W未來短期利率預測偏誤(%)……………………………...50
附表4-1：BDT期初結構密合偏誤(%)…………………..…………..….51
附表4-2：BDT未來短期利率預測偏誤(%)…………………………… …51
附表4-3：H-W期初結構密合偏誤(%)………………………………...…51
附表4-4：H-W未來短期利率預測偏誤(%)……………..……………….52
附表5-1：BDT期初結構密合偏誤(%)……………….……………………52
附表5-2：BDT未來短期利率預測偏誤(%)……….….………………….52
附表5-3：H-W期初結構密合偏誤(%)………………………………….…53
附表5-4：H-W未來短期利率預測偏誤(%)……………………………….53
附表6-1：BDT期初結構密合偏誤(%)…………………..……………….53
附表6-2：BDT未來短期利率預測偏誤(%)……………….………………54
附表6-3：H-W期初結構密合偏誤(%)…………………..……………….54
附表6-4：H-W未來短期利率預測偏誤(%)……………..……………...54
附表7-1：BDT期初結構密合偏誤(%)……………….………………....55
附表7-2：BDT未來短期利率預測偏誤(%)……….….………………….55
附表7-3：H-W期初結構密合偏誤(%)…………………..……………...55
附表7-4：H-W未來短期利率預測偏誤(%)…………………………….…56
附表8-1：BDT期初結構密合偏誤(%)…………………..……………….56
附表8-2：BDT未來短期利率預測偏誤(%)…………….………………..56
附表8-3：H-W期初結構密合偏誤(%)………………………………….…57
附表8-4：H-W未來短期利率預測偏誤(%)……………..……………...57
附表9-1：BDT期初結構密合偏誤(%)……………….………………..…57
附表9-2：BDT未來短期利率預測偏誤(%)……….….……………….…58
附表9-3：H-W期初結構密合偏誤(%)……………………………….....58
附表9-4：H-W未來短期利率預測偏誤(%)……………………………….58
附表10-1：BDT期初結構密合偏誤(%)…………………..………………59
附表10-2：BDT未來短期利率預測偏誤(%)………………………………59
附表10-3：H-W期初結構密合偏誤(%)…………………..……………..59
附表10-4：H-W未來短期利率預測偏誤(%)……………..………………60
圖目錄
圖1：研究流程圖……………………………………………………………4
圖2：均數復歸圖……………………………………………….…………16
圖3：三元利率樹狀圖…………………………………….…..…………18
圖4：三元樹結點圖………………………….…………….………..….19
圖5：一期的樹狀圖…………………………….…….……..………….21
圖6：二元樹樹狀圖…………………………………….…………………22
圖7：Black-Derman-Toy短期利率圖……………….…….………….…24

參考文獻
一、 中文部分
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2、邱文飛，1996，利率期限結構模型之數值解與封閉解的比較，國立臺灣大學商學研究所，碩士論文。
3、徐俊明，1997，投資學理論與實務，新陸書局股份有限公司出版。
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5、張菁芬，1997，利率結構三元樹與二元樹架構之比較研究，國立臺灣大學國際企業學研究所，碩士論文。
6、滑明曙，1997，選擇權估價理論，華泰文化事業有限公司出版。
7、謝劍平，1997，財務管理，智勝文化事業有限公司出版。
8、蘇金祥，1998，Hull and White三元利率樹連續時間解與間斷時間解之數值分析，國立台灣大學財務金融研究所，碩士論文
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