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    政大機構典藏 > 商學院 > 金融學系 > 學位論文 >  Item 140.119/31154
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/31154


    Title: 利率連動債券之評價與分析-BGM模型
    Authors: 張欽堯
    Contributors: 廖四郎
    張欽堯
    Keywords: BGM模型
    LIBOR市場模型
    二元樹
    利率連動債券
    BGM Model
    LIBOR Market Model
    Recombining Binomial Tree
    Structure Notes
    Date: 2003
    Issue Date: 2009-09-14 09:26:36 (UTC+8)
    Abstract: 傳統上描述利率期間結構,不外乎藉由瞬間短期利率的隨機過程(如:Hull and White模型),或瞬間遠期利率的隨機過程(如:HJM模型)。應用這些方式理論上雖然可行,但是市場上並無法觀察得知這些瞬間利率。

    Brace-Gatarek-Musiela利率模型(簡稱BGM模型)是將HJM模型間斷化,直接推導市場上可觀察得到之LIBOR利率的隨機過程,用它來描述市場利率期間結構,並利用數學的技巧,推導出符合對數常態的型式,方便使用Black公式來求解,且同時考慮LIBOR利率之波動程度,透過與市場資料的校準,符合市場上的利率期間結構及利率波動結構,有助於利率衍生性商品的訂價與避險。

    由於市場上有愈來愈多的利率衍生性商品,不是由單純的cap、swaption來組成,例如:路徑相依選擇權、美式選擇權、回顧型選擇權…等,這些新奇選擇權要求出評價公式很難,所以通常使用數值方法來評價。常用的數值方法有蒙地卡羅模擬法及樹狀圖評價法,由於使用蒙地卡羅模擬法處理起來較耗時,而且評價美式選擇權比較麻煩,而樹狀圖評價法較省時,且應用較廣。因此,本文除了詳細推導BGM利率模型,並建構出BGM利率模型下的利率樹,來對這些新奇選擇權做評價。

    最後做一實證分析,以市場上的所發行的利率連動債券為例,對於匯豐銀行美元護本109利率連動債券的設計、評價、損益分析及其相關議題做詳盡的探討。
    Reference: 1、方姿云(2003),市場模型於歐洲美元期貨選擇權之評價,東華大學 企業管理學研究所碩士論文。
    2、吳香瑩(2003),逆浮動Libor利率連動債券評價與避險,政治大學金融研究所碩士論文。
    3、陳兆維(2002),利率波動結構對標準與平均利率上限契約評價的影響,台灣大學財務金融學研究所碩士論文。
    4、陳彥禎(2003),路徑相依及報償修改型利率連動債券之設計及分析,政治大學金融研究所碩士論文。
    5、戴維志(2003),HJM模型和市場模型於歐洲美元期貨選擇權評價之理論分析,東華大學國際經濟研究所碩士論文。
    6、船山幸一郎(2001),ボラティリティ・スマイルを考慮したLIBORマーケットモデル,東京工業大学大学院情報理工学研究科・数理計算科学専攻修士論文。
    7、Andersen, L.,and J. Andreasen,(2000),”Volatility skews and extensions of the Libor market model.”, Applied Mathematical Finance, 7, 1-30.
    8、Black, F.,(1976), “The Pricing of Commodity Contracts.” Journal Financial Economics, 3, 167-179.
    9、Brace, A., D. Gatarek, and M. Musiela,(1997),”The Market Model of Interest Rate Dynamics.”, Mathematical Finance, 7,127-155.
    10、Cox, J.C., J.E. Ingersoll, Jr., and S.A. Ross,(1985),”A theory of the term structure of interest rates.” Econometrica, 53, 385-407.
    11、Heath, D., R. Jarrow, and A. Morton,(1990),”Bond pricing and the term structure of interest rates: a discrete time approximation.” The Journal of Financial and Quantitative Analysis, 25, 419-440.
    12、Heath, D., R. Jarrow, and A. Morton,(1992),”Bond Pricing and The Term Structure of Interest Rates:A New Methodology for Contingent Claims Valuation.”, Econometrica, 60,77-105.
    13、Ho, T.S.Y., and S.B. Lee,(1986),”Term structure movements and pricing interest rate contingent claims.” Journal of Finance, 41, 1011-1029.
    14、Hull, J.C. and A. White,(1990),”Pricing interest-rate-derivative securities.” Review of Financial Studies, 3, 423-440.
    15、Hull, J.C. and A. White,(1993),”Bond option pricing based on a model for the evolution of bond prices.” Advances in Futures and Options Research, 6, 1-13.
    16、Hull, J. , and A. White,(2000), “Forward Rate Volatilities, Swap Rate Volatilities, and The Implementation of The LIBOR Market Model”, Journal of Fixed Income, 9, 46-62.
    17、Jamshidian, F.,(1997),”LIBOR and Swap Market Models and Measures.”, Finance and Stochastics, 1, 293-330.
    18、Miltersen, K., K. Sandmann, and D. Sondermann,(1997),”Closed Form Solutions for Term Structure Derivatives with Lognormal Interest Rates.”,Journal of Finance, 52, 409-430.
    19、Stapleton, D., and R. Stapleton,(2003),”The LIBOR Market Model A Recombining Binomial Tree Methodology”, Working paper.
    20、Uratani, T.and M. Utsunomiya,(1999),”Lattice Calculation for Forward LIBOR Model.” Working paper.
    21、Vasicek, O.,(1977),” An Equilibrium Characterization of the Term Structure.”,Journal of Financial Economics, 5, 177-188.
    Description: 碩士
    國立政治大學
    金融研究所
    91352007
    92
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0091352007
    Data Type: thesis
    Appears in Collections:[金融學系] 學位論文

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