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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/59970


    Title: 在BGM 模型下固定交換利率商品之效率避險與評價
    An efficient valuation and hedging of constant maturity swap products under BGM model
    Authors: 蔡宏彬
    Contributors: 廖四郎
    蔡宏彬
    Keywords: 固定交換利差選擇權
    固定交換輪棘選擇權
    LIBOR市場模型
    避險
    CMS spread option
    CMS ratchet option
    LIBOR market model
    hedge
    Date: 2009
    Issue Date: 2013-09-04 10:08:34 (UTC+8)
    Abstract: 傳統上在 LIBOR市場模型架構下,評價固定交換商品一般是透過模地卡羅模擬。在本文中,吾人在此模型架構下推導出一個遠期交換利率的近似動態,並在一因子的架構下提供一個固定交換利差選擇權與固定交換輪棘選擇權的近似評價公式。數值結果顯示這兩者之相對誤差甚小。此外對於這兩個產品,吾人亦提供一個有效率的避險方法。
    The derivatives of the constant maturity swap (CMS) are evaluated by the LIBOR market model (LMM) implemented by Monte Carlo methods in the previous researches. In this paper, we derive an approximated dynamic process of the forward-swap rate (FSR) under LMM. Based on the approximated dynamics for the FSR under one factor model, CMS spread options and CMS ratchet options are valued by the no-arbitrage method in approximated analytic formulas. In the numerical analysis, the relative errors between the Monte Carlo simulations and the approximated closed form formulas are very small for CMS spread options and CMS ratchet options and we also provide an efficient hedging method for these products under one factor LMM.
    Reference: Brace, A., Dun, T. A., and Barton, G., (1998). “Toward a central interest rate model.” in Handbooks in Mathematical Finance, Topics in Option Pricing, Interest Rates and Risk Management, Cambridge University Press.

    Brace, A., Gatarek, D., and Musiela, M., (1997). “The Market Model of Interest Rate Dynamics.” Mathematical Finance 7, 127-155.

    Brigo, D., and Mercurio, F., (2006). Interest Rate Models: Theory and Practice. Second Edition, Springer Verlag.
    Galluccio, S., and Hunter, C., (2004). “The co-initial swap market model,” Economic Notes 33, 209-232.

    Heath, D., Jarrow, R., Merton, A., (1992). “Bond Pricing and the Term Structure of Interest Rate: A new Methodology for Contingent claims Valuation”, Economitrica, 60, 77-105

    Hunter, C. J., Jackel, P. and Joshi, M. S., (2001). “Drift approximations in a forward-rate-based LIBOR market model,” Risk Magazine 14.
    Hull, J., and White, A., (1999). “Forward rate volatilities, swap rate volatilities, and the implementation of the LIBOR market model,” Journal of Fixed Income 10, 46-62.

    Jamshidian, F., (1997). “LIBOR and swap market model and measure,” Finance and Stochastics 1, 293-330.

    Mercurio, F., and Pallavicini, A., (2005). “Mixing Gaussian models to price CMS derivatives,” Working paper.

    Musiela, M. and Rutkowski, M., (1997). “Continuous-time term structure models:a forward measure approach.” Finance Stochast 1, 261-291

    Rebonato, R., (2004) Volatility and Correlation: The Perfect Hedger and the Fox. Second Edition. John. Wiley & Sons, New York.
    Description: 博士
    國立政治大學
    金融研究所
    903525058
    98
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0903525084
    Data Type: thesis
    Appears in Collections:[Department of Money and Banking] Theses

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