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| 研究生： |
蔡宏彬 |
|---|---|
| 論文名稱： |
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 |
| 指導教授： | 廖四郎 |
| 學位類別： |
博士
Doctor |
| 系所名稱： |
商學院 - 金融學系 Department of Money and Banking |
| 論文出版年： | 2010 |
| 畢業學年度： | 98 |
| 語文別： | 中文 |
| 論文頁數： | 51 |
| 中文關鍵詞： | 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 |
| 外文關鍵詞： | CMS spread option, CMS ratchet option, LIBOR market model, hedge |
| 相關次數： | 點閱：139 下載：30 |
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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.
Chapter 1 Introduction p1
Chapter 2 The LIBOR and Swap Market Models p4
2.1 Introduction p4
2.2 The Dynamics of Forward-LIBOR Rate under Adjusted Forward Measure p6
2.3 Monte Carlo Pricing of Constant Maturity Swap Products with LIBOR Market Model p9
Chapter 3 The Approximated dynamics of Constant Maturity Swap Products p12
3.1 Model p12
3.2 Constant Maturity Swap products p16
Chapter 4 Valuation of Constant Maturity Swap Products p18
4.1 Valuation of Constant Maturity Swap spread options p20
4.2 Valuation on Constant Maturity Swap ratchet options p21
Chapter 5 Calibration Procedure and Numerical analysis p24
5.1 parameters setting and calibration procedure p24
5.2 The closed-form formula vs Monte Carlo simulation p26
5.3 Delta Hedge p28
Chapter 6 Conclusions p30
Reference p31
Appendix A: Proof of Lemma 4.1. p32
Appendix B.1: Leibniz’s rule p41
Appendix B.2: Proof of theorem 5.1. p43
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.
