許多公司在發行公司債的時候，會給此公司債一個可提前贖回的特性，此種公司債稱為可贖回公司債(Callable Bond)，用來規避利率變動風險的金融商品也與我們熟知的利率交換不同，稱為可取消利率交換(Cancelable Swap)。其實可取消利率交換可以拆解成百慕達利率交換選擇權(Bermudan Swaption)加上利率交換，由於利率交換之評價較簡單也有市場一致的評價方法，因此百慕達利率交換選擇權便成為評價的重點。
評價的部分，由於百慕達式的商品有提前履約的特性，造成其封閉解不存在，因此需要利用其他的近似解或是數值方法來求它的價格。由於本文採用BGM(1997)的市場利率模型(Libor Market Model)，其高維度的性質導致數狀方法與有限差分法使用起來較無效率，因此本文選擇使用蒙地卡羅法做為評價的方法，同時利用Longstaff and Schwartz(2001)的最小平方蒙地卡羅法(Least Squares Monte Carlo Method)來解決提前履約的問題。
最後，本文將採用2種利率波動度假設與2種不同利率間相關係數的假設，共4種組合，在歐式利率交換選擇權的市場波動度下進行校準，使用校準出來的參數進行評價來得到4種價格。再進行商品的敏感度分析(Sensitivity Analysis)和風險值(Value at Risk)的計算。

There are some corporate bonds which can be called back at specified time. Those bonds are called Callable Bond. The hedging instruments for those bonds are called Cancelable Swap. In fact, Cancelable Swap consist of Bermudan Swaption and Swap. The pricing of Swap is easy, so the pricing of Bermudan Swaption is the important point of this paper.
The closed form solution of those products don’t exist due to the unknown strike time. And, the Libor Market Model is high dimension, leading to the inefficiency of Tree Method and Finite Difference Method. Therefore, we used Least Squares Monte Carlo Method published by Longstaff and Schwartz(2001).
Finally, we used two volatility models and two correlation coefficient models. We did calibration with the market price of European Swaption and then priced Bermudan Swaption. Moreover, we also calculated Sensitivity Analysis and Value at Risk.

中文文獻
[1] 王祥帆 (2005) 百慕達式利率交換選擇權。
[2] 蔡宏彬 (2009) 在BGM模型下固定交換利率商品之效率避險與評價。

英文文獻
[1] Alpsten, H., (2003), Pricing bermudan swap options using the BGM model with arbitrage – free discretisation and boundary based option exercise, Working paper, Department of mathematics royal institute of technology.
[2] Andersen, L., (2000), A Simple Approach to the Pricing of Bermudan Swaptions in the Multi – Factor Libor Market Model, Journal of Computational Finance 3(2), 1-32.
[3] Brace, A., D. Gatarek, and M. Musiela, (1997), The market model of interest rate dynamics, Mathematical Finance 7(2), 127-155.
[4] Brigo, D. and Mercurio, F. (2007). Interest rate models, theory and practice, Springer Science + Business Media.
[5] Cox, J., Ingersoll J. and Ross, S. A theory of the term structure of interest rates, Econometrica, 53(2) (1985) 385-407.
[6] Coffey, C. and Schoenmakers, J(2002). Systematic generation of parametric correlation structures for the libor market model, International Journal of Theoretical and Applied Finance.
[7] Glasserman, P. (2004). Monte carlo methods in financial engineering, Springer Science + Business Media.
[8] Hull, J., White, A. (1993). One-factor interest rate models and the valuation of interest rate derivative securities. Journal of Financial and Quantitative Analysis 28, 235-254.
[9] Jorion, P. (1997): Value at Risk – The New Benchmark for Controlling Market Risk. McGraw-Hill, New York
[10] Lvov, D. (2005). Monte carlo methods for pricing and hedging: Applications to bermudan swaptions and convertible bonds, PhD dissertation, ISMA Centre, University of Reading.
[11] Longstaff, F. A., and Schwartz, E. S. (2001), “Valuing American Potions by Simulation: A Simple Least – Squares Approach”, The Review of Financial Studies 14(1), 113-147.
[12] Pedersen, M. B, (1999), Bermudan Swaptions in the LIBOR market model, Financial Research Department, Preprint.
[13] Pietersz, R. and A. Pelsser, (2003), Risk managing bermudan swaptions in the LIBOR BGM Model, Preprint.
[14] Piterbarg, V. (2005). A practitioner’s guide to pricing and hedging callable libor exotics in forward libor models, Working paper.
[15] Rebonato, R. (2002). Modern pricing of interest rate derivatives: The libor market model and beyond, Princeton University Press.
[16] Steffen Hippler, (2008). Pricing bermudan swaptions in the LIBOR market model, master dissertation, university of Oxford.
[17] Svoboda, S., (2004), Interest rate modelling, published by Palgrave Macmillan.
[18] Tavella, D., (2002), Quantitative methods in derivatives pricing: An Introduction to Computational Finance, Published by John Wiley & Sons, Ltd.
[19] Vasicek, O. (1997), An equilibrium characterization of the term structure, Journal of Financial Economics 5, 177-188.
[20] Weigel, P., (2004), Optimal calibration of LIBOR market models to correlations, The Journal of Derivatives, Winter 2004, 43-50.