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題名 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作者 蔡宏彬 貢獻者 廖四郎
蔡宏彬關鍵詞 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日期 2009 上傳時間 4-Sep-2013 10:08:34 (UTC+8) 摘要 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.參考文獻 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, 261-291Rebonato, R., (2004) Volatility and Correlation: The Perfect Hedger and the Fox. Second Edition. John. Wiley & Sons, New York. 描述 博士
國立政治大學
金融研究所
903525058
98資料來源 http://thesis.lib.nccu.edu.tw/record/#G0903525084 資料類型 thesis dc.contributor.advisor 廖四郎 zh_TW dc.contributor.author (Authors) 蔡宏彬 zh_TW dc.creator (作者) 蔡宏彬 zh_TW dc.date (日期) 2009 en_US dc.date.accessioned 4-Sep-2013 10:08:34 (UTC+8) - dc.date.available 4-Sep-2013 10:08:34 (UTC+8) - dc.date.issued (上傳時間) 4-Sep-2013 10:08:34 (UTC+8) - dc.identifier (Other Identifiers) G0903525084 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/59970 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融研究所 zh_TW dc.description (描述) 903525058 zh_TW dc.description (描述) 98 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents Chapter 1 Introduction p1Chapter 2 The LIBOR and Swap Market Models p42.1 Introduction p42.2 The Dynamics of Forward-LIBOR Rate under Adjusted Forward Measure p62.3 Monte Carlo Pricing of Constant Maturity Swap Products with LIBOR Market Model p9Chapter 3 The Approximated dynamics of Constant Maturity Swap Products p123.1 Model p123.2 Constant Maturity Swap products p16Chapter 4 Valuation of Constant Maturity Swap Products p184.1 Valuation of Constant Maturity Swap spread options p204.2 Valuation on Constant Maturity Swap ratchet options p21Chapter 5 Calibration Procedure and Numerical analysis p245.1 parameters setting and calibration procedure p245.2 The closed-form formula vs Monte Carlo simulation p265.3 Delta Hedge p28Chapter 6 Conclusions p30Reference p31Appendix A: Proof of Lemma 4.1. p32Appendix B.1: Leibniz’s rule p41Appendix B.2: Proof of theorem 5.1. p43 zh_TW dc.format.extent 374036 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0903525084 en_US dc.subject (關鍵詞) 固定交換利差選擇權 zh_TW dc.subject (關鍵詞) 固定交換輪棘選擇權 zh_TW dc.subject (關鍵詞) LIBOR市場模型 zh_TW dc.subject (關鍵詞) 避險 zh_TW dc.subject (關鍵詞) CMS spread option en_US dc.subject (關鍵詞) CMS ratchet option en_US dc.subject (關鍵詞) LIBOR market model en_US dc.subject (關鍵詞) hedge en_US dc.title (題名) 在BGM 模型下固定交換利率商品之效率避險與評價 zh_TW dc.title (題名) An efficient valuation and hedging of constant maturity swap products under BGM model en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 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, 261-291Rebonato, R., (2004) Volatility and Correlation: The Perfect Hedger and the Fox. Second Edition. John. Wiley & Sons, New York. zh_TW
