臺灣博碩士論文加值系統

本文主要目的係探討利率衍生性商品之樹狀圖評價，從利率模型之選擇、短期利率樹狀圖投入值(殖利率與遠期利率曲線)之配適、至利率衍生性商品(以利率交換選擇權為例)之評價及其敏感度分析等，提出完整之討論。研究重點分別為：
1、 探討殖利率與遠期利率曲線之配適問題，並對Adams and Deventer (1994)之最大平滑度遠期利率曲線配適模型，進行理論性質之深入探討及國內資料之實證研究。
2、 以樹狀圖法評價利率交換選擇權及履約價可重設之重設利率交換選擇權，並分別對其進行參數敏感度分析。
研究結果如下：
1、 最大平滑度遠期利率曲線配適方法之理論探討方面：首先指出Adams and Deventer模型在求解上之問題，並提出另一種找尋適當條件式之方法以擴大該模型之適用範圍；接著，嘗試修改其最大平滑度之定義(將極小化總曲度改為極小化總斜率)及樣本型態(將零息債券改為附息債券)，然而卻無法求解，顯示Adams and Deventer模型仍以維持原設定為佳；另在函數可能型態之探討上則發現，多項式型態之遠期利率或殖利率曲線實為此種配適方法之必然結果；最後，將該模型應用於配適一條最大平滑度之殖利率曲線，函數型態仍為不含二、三次項之四次多項式。實證研究方面，則分別利用國內之票券、台幣利率交換、及政府債券資料配適遠期利率曲線，並以台幣利率交換資料配適殖利率曲線。
2、 以樹狀圖法建構無套利機會之利率模型，進而評價利率交換選擇權及重設利率交換選擇權。主要特色是應用Jamshidiam(1991)所提出之向前推導法(forward induction)，透過Arrow-Debreu證券價格進行評價。此作法具有運算效率、及可處理衍生性商品價值與過去路徑相依(如重設利率交換選擇權)之評價問題等優點。
3、 分別對利率交換選擇權評價模型中：利率交換之固定利率(即選擇權之履約價)、殖利率曲線、利率波動曲線、均數復歸(mean reversion)曲線，以及重設利率交換選擇權之重設價位與重設固定利率等參數進行敏感度分析，觀察歐式與百慕達式利率交換選擇權價值及其變動量、與兩者之價差受上述參數值變動之影響；至於評價模型收斂性之探討上則發現，樹狀圖期數(time steps)較少時之價值有低估現象，且期數越少或固定利率值越高時低估越嚴重，此情形又以歐式利率交換選擇權較百慕達式明顯。

This study shows a comprehensive discussion on using the tree method to price interest rate derivatives. This includes the process which begins with choosing a suitable interest rate model, fitting the yield curves or forward rate curves as the input data for a tree, pricing the interest rate derivatives, taking interest rate swaptions for example, to their sensitivity analyses. The main purposes of this study are presented as following :
1、 Explore the issue of fitting yield curves and forward rate curves. Further analysis on the theoretical essence of the Adams and Deventer model (1994), which fits the forward rate curves with maximum smoothness, as well as the empirical study using Taiwan''s market data are included.
2、 Show a tree method for pricing interest rate swaptions and reset swaptions, which allows for the resetting of the strike price. Moreover, the sensitivity analyses of their parameters are studied.
The findings of this study are as follows :
1、 On the theoretical side, the essence of the model for fitting forward rate curves with maximum smoothness is studied : The problem of solving simultaneous equations in the Adams and Deventor model (1994) is figured out, therefore, an approach for finding suitable conditions is introduced to extend the application of the model. Some revisions of the model''s specifications are tried, such as using coupon bond data instead of zero-coupon bond data and changing the measure of maximum smoothness by minimizing total slopes instead of total curvatures. While the study results suggest that the original specifications should remain. This model may also be applied to fit a yield curve with maximum smoothness, its functional form is also derived to be a fourth-degree polynomial with cubic term absent. As for the possibility of other functional forms of forward rate curves or yield curves, this study''s findings show that a polynomial function is an inevitable result in this model. On the empirical side : domestic commercial paper, NT dollar interest rate swaps (IRS), and government bond data are used to fit the forward rate curves respectively. NT dollar IRS data is used to fit a yield curve.
2、 A No-arbitrage interest rate model is implemented by using a tree method. Furthermore, interest rate swaptions and reset swaptions are evaluated. Using the Arrow-Debrue security price and the forward induction technique provided by Jamshidiam (1991) to price interest rate swaptions, this study improves the computing efficiency for constructing a short rate tree. Also, the tough pricing problem that the value of derivatives are path-dependent to their past paths, such as reset interest rate swaptions in this study, could be handled with this pricing method.
3、 The sensitivity analyses of swaption parameters are studied to observe how the European and Bermudan swaptions values, the changes of their values, and the differences between them are influenced by changing the parameters. These parameters include the fixed rates of interest rate swaps (equivalent to strike price of option), yield curves, volatility curves, mean reversion curves, the reset rates and reset fixed rates of reset swaptions. As for the convergence of the pricing model, the findings of the study are that : prices are undervalued for small time steps; the smaller the time steps and the higher the fixed rate, the more it''s undervalued; and these phenomena are more obvious for European swaptions than Bermudan swaptions.

封面
謝詞
中文摘要
英文摘要
目錄
圖表目錄
研究架構圖
第一章 緒論
第一節 研究動機與研究重點
第二節 研究架構
第二章 利率模型及其建構方法之分析
第一節 前言
第二節 利率模型分析
第三節 利率模型之建構方法
第三章 殖利率曲線與遠期利率曲線配適方法之分類與比較
第一節 前言
第二節 殖利率曲線配適方法之分類與整理
第三節 遠期利率曲線配適方法之分類與整理
第四節 結論
第四章 最大平滑度遠期利率曲線配適模型之再探討
第一節 前言
第二節 Adams and Deventer模型之再探討
第三節 實證方法與結果
第四節 結論
第五章 利率交換選擇權之樹狀圖評價法
第一節 前言
第二節 利率交換、利率交換選擇權、及可贖回/可賣回債券
第三節 利率交換選擇權評價法之數值範例
第四節 「履約價重設之利率交換選擇」及其評價法
第六章 利率交換選擇權參數敏感度分析之實證研究
第一節 實證方法與資料來源
第二節 利率交換選擇權之參數敏感度分析
第三節 重設利率交換選擇權之參數敏感度分析
第四節 結論
第七章 結論與後續研究方向
附錄

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