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研究生:梁錫弘
研究生(外文):Ryan Hsi-Hung Liang
論文名稱:在CIR模型下各種債券策略的比較
論文名稱(外文):Comparison of Different Bond Portfolio Strategies under CIR Term Structure Model
指導教授:曾郁仁曾郁仁引用關係
指導教授(外文):Larry Yu-Ren Tzeng
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:財務金融學研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:34
中文關鍵詞:免疫策略存續期間
外文關鍵詞:MacaulayDurationCIR Term Structure ModelImmunization
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論文名稱:在CIR模型下各種債券策略的比較
校所別: 國立台灣大學財務金融學研究所
畢業期間:九十年度第二學期
提要別: 碩士學位論文提要
研究生: 梁錫弘
指導教授:曾郁仁 博士
頁數:  34頁
論文提要內容:
  Duration的概念在1938年被Macaulay提出之後,即使它有一些不合理的假設,如YTM曲線須為直線及每期YTM的變化量均須相同等等。但由於其計算上的便利性,所以仍廣泛地被實務界應用在許多債券評價或是免疫策略等執行上。但實際世界的利率走勢並不如Macaulay世界般一樣地單純,如果完全以該理論的模式為策略執行的依歸,其績效勢必不如預期。
  本文嘗試著將Macaulay世界的假設放寬,並以CIR (1985) term structure model為基礎,透過模擬利率路徑的結果,來當做實際世界利率的預測值。並藉由在CIR模型下導出之新的Duration的概念,重新執行免疫策略及我們所設計的另一種積極型的債券策略。最後發現在這樣不同的設定下,CIR免疫策略的績效會優於積極型的債券策略及傳統Macaulay的免疫策略。
  本文的第一章簡單地陳述Duration概念的由來及免疫策略的發展;第二章說明本篇文章發表的動機。在第三章中對於布朗運動及CIR模型的原理及其理論背景做了一些詳細的描述;第四章,我們定義在本文中所用到的CIR Duration及各種債券策略的執行方法;第五章及第六章則是本文所得到的結果及我們所歸納出來的結論。

Graduate Date: June 2002
Title of Dissertation: Comparison of Different Bond Portfolio Strategies under CIR Term Structure Model
Name of Institute: Graduate Institute of Finance, Nation Taiwan University
Name of Student: Ryan Hsi-Hung Liang
Advisor: Dr. Larry Yu-Ren Tzeng
Degree Conferred: Master
Total Pages: 34 Pages
Abstract:
Macaulay duration is widely used to measure the risk behavior of bond portfolio in recently years, even though these unreasonable assumptions including the flat YTM curve and change by the same amount at different period. In the real world, interest rate fluctuates not mildly and not predictably, Macaulay duration really could not be able to catch the true characteristic for interest rate movement. Therefore, Macaulay immunization strategy could lose their function and would not get a satisfied performance.
Under these assumptions of CIR term structure model, this article presents a new duration concept and compares performance of different bond strategies by using simulation method. The results display the CIR passive strategy will get a better performance if interest rates of real world move like the behaviors of CIR model described.

Contents
1.Introduction...............................................1
2.Motivation.................................................3
3.Background.................................................4
3.1 Brownian Motion........................................4
3.1.1 History..........................................4
3.1.2 Definition.......................................4
3.1.3 Application......................................5
3.2 Cox-Ingersoll-Ross interest rate model.................6 
3.2.1 History..........................................6
3.2.2 Definition.......................................7
4.Methodology................................................8
4.1 Definition of duration under CIR interest rate model...8
4.2 Strategy assumptions and implementations..............10
5.Results...................................................13
5.1 Duration under CIR model..............................13
5.2 Results for interest rate simulation..................15
5.3 Results for different bond portfolio’s strategies....17
6.Conclusion................................................31
Reference...................................................33

Reference
1. Bierwag, G. O. “Immunization, duration, and the term
structure of interest rates”, Journal of Financial and
Quantitative Analysis 12 (December), 1977.
2. Bierwag, G. O. “Duration Analysis — Managing Interest Rate
Risk.” Cambridge: Ballinger, 1987.
3. Cox, John. Ingersoll, Jonathan. Ross, Stephen. “Duration
and the measurement of basis risk”, Journal of Business,
Volume 52, Issue 1 (Jan., 1979), 1979.
4. Cox, John. Ingersoll, Jonathan. Ross, Stephen. “A Theory of
the Term Structure of Interest Rates.” Econometrica 53
(March 1985), 1985.
5. Cox, John. Ingersoll, Jonathan. Ross, Stephen. “An
Intertemporal General Equilibrium Model of Asset Prices.”
Econometrica 53 (1985), 1985.
6. Fisher, L., and Weil, R. L. “Coping with the risk of
interest-rate fluctuations”. Journal of Business 44
(October) 1971.
7. Gagnon, L. and L. D. Johnson, “Dynamic Immunization under
Stochastic Interest Rates”, The Journal of Portfolio
Management, spring 1994.
8. Hicks, John R., “Value and Capital” Oxford: Clarendon
Press 1939.
9. Hull, John C. “Options, Futures, & Other Derivatives,
fourth edition”, published by Prentice Hall International,
Inc, 2000. Page 564-570.
10.Macaulay, Frederick, R., “Some Theoretical Problems
Suggested by the Movement of Interest Rates, Bonds, Yields,
and Stock Prices in the United States since 1856,” New
York, Columbia University Press 1938.
11.Rebonato, Riccardo. “Interest-Rate Option Models,”
published by John Wiley & Sons, 1998. Page 233-257.
12.Samuelson, Paul A., “The Effects of Interest Rates
Increases on The Banking System,” American Economic Review,
March 1945.
13.Vasicek, O. A. “An Equilibrium Characterization of the Term
Structure,” Journal of Financial Economics, 5. 1977.
14.Wallas, G. E. “Immunization”, Journal of Institute of
Actuaries Students Societies, 1960.

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