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    題名: 可贖回雪球式商品的評價與避險
    作者: 曹若玹
    貢獻者: 廖四郎
    曹若玹
    關鍵詞: 利率連動債券
    最小平方蒙地卡羅
    參數校準
    提前贖回
    避險參數
    BGM
    LFM
    LIBOR
    Greeks
    calibration
    snowball
    Sausage Monte Carlo
    pathwise
    日期: 2005
    上傳時間: 2009-09-17 19:02:32 (UTC+8)
    摘要: 本文採用Lognormal Forward LIBOR Model (LFM) 利率模型,針對可贖回雪球式債券進行相關的評價與避險分析,而由於此商品的計息方式為路徑相依型態,價格沒有封閉解,故必須利用數值方法來進行評價。過去通常使用二元樹或三元樹的方法來評價具有可贖回特性的商品,但因為LFM是屬於多因子模型,所以不容易處理建樹的過程。而一般路徑相依商品的評價是使用蒙地卡羅法來進行,但是標準的蒙地卡羅法不易處理美式或百慕達式選擇權的問題,因此,本研究將使用由Longstaff and Schwartz(2001)所提出的最小平方蒙地卡羅法,來處理同時具有可贖回與路徑相依特性的商品評價並進行實證研究。

    <br>此外,關於可贖回商品的避險參數部分,由於商品的價格函數不具有連續性,若在蒙地卡羅法之下直接使用重新模擬的方式來求算避險參數,將會造成不準確的結果,而Piterbarg (2004)提出了兩種可用來計算在LFM下可贖回商品避險參數的方法,其實証結果發現所求出的避險參數結果較準確,因此本研究將此方法運用至可贖回雪球式利率連動債券,並分析各種參數變化對商品價格的影響大小,便於進行避險工作。
    參考文獻: [1] Brace, A., D. Gatarek and M. Musiela (1997). The Market Model of Interest Rate . Dynamics Mathematical Finance 7, 127-155.
    [2] Brigo, D. and F. Mercurio (2001). Interest Models, Theory and Practice. Springer-Verlag.
    [3] Carol Alexander(2003). Common Correlation and Calibrating the Lognormal Forward Rate Model . ISMA Discussion Papers in Finance 2002-18. To appear in Wilmott Magazine.
    [4] Glasserman, P. (2004). Monte Carlo Method in Financial Engineering. New York,Springer.
    [5] Glasserman, P., and X., Zhao (1999). Fast Greeks by Simulation in Forward LIBOR Models, Journal of Computational Finance 3, 5-39.
    [6] Glasserman, P., and Yu, B.(2004). Number of Paths Versus Number of Basis Functions in American Option Pricing. Annuals of Applied Probability 14(4), 2090-2119.
    [7] Jamshidian, F. (1997). LIBOR and Swap Market Models and Measures . Finance and Stochastics 1, 293-330.
    [8] Longstaff, F. and Schwartz, E. (2001).Valuing American Options by Simulation: A Simple Least-Squares Approach. The Review of Financial Studies, Vol. 14, No.1, p.113-147.
    [9] Piterbarg.V.V.(2003). A Practioner’s Guide to Pricing and hedging Callable Libor Exotics in Forward Libor Models, SSRN Working Paper.
    [10] Piterbarg.V.V.(2004a). Computing Deltas of Callable Libor Exotics in Forward Libor Models. Journal of Computational Finance 7(3),107-144.
    [11] Piterbarg.V.V.(2004b). Pricing and Hedging Callable Libor Exotics in Forward Libor Models. Journal of Computational Finance 8(2), 65-117.
    [12] Rebonato, R. (1998). Interest Rate Option Models. Second Edition. Wiley, Chichester.
    [13] Rebonato, R. (1999). Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options, John Wiley & Sons Ltd., West Sussex.
    [14] Rebonato, R.(1999). On the Simultaneous Calibration of Multifactor Lognormal Interest Rate Models to Black Volatilities and to the Correlation Matrix, The Journal of Computational Finance,2, 5-27.
    [15] Rebonato, R (2002), Modern Pricing of Interest-Rate DerivativesL:The LIBOR Market Model and Beyond. Princeton University. Press, Princeton.
    [16] Schoenmakers, J. and C., Coffet (2000). Stable Implied Calibration of a Multi-factor Libor Model via a Semi-parametric Correlation Structure, Weierstress Institute Preprint no.611.
    [17] Shreve, S. (2004). Stochastic Calculus for Finance II, Springer-Verlag, New York.
    [18] Svoboda, S. (2004). Interest Rate Modelling , Palgrave Macmillan, New York.
    描述: 碩士
    國立政治大學
    金融研究所
    93352009
    94
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0093352009
    資料類型: thesis
    顯示於類別:[金融學系] 學位論文

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