臺灣博碩士論文加值系統

Cox-Ingersoll-Ross(CIR)模型是個常見的短期利率模型，描述利率隨時間的變化。Nawalkha與Beliaeva提供了基於CIR模型的三元樹方法，能夠有效率的評價零息債券。本論文採用另一種Dai與Lyuu的三元樹方法，使得債券價格有較平滑的收斂行為。

The Cox–Ingersoll–Ross (CIR) model is a popular short rate model. Nawalkha and Beliaeva propose a trinomial tree for the CIR model to price zero-coupon bonds efficiently. This thesis proposes a different trinomial tree based on Dai and Lyuu. This results in smoother convergence.

口試委員會審定書 i
誌謝 ii
中文摘要 iii
英文摘要 iv
第一章 緒論 1
第二章 文獻回顧 2
2.1 Cox-Ingersoll-Ross 模型 2
2.2 Nelson-Ramaswamy 轉換 2
2.3 Nawalkaha-Beliaeva 三元樹 3
2.4 Dai-Lyuu 二元三元樹 3
第三章 實驗方法 4
3.1 三元樹方法 4
3.2 預先找出截斷位置 6
3.3 債券選擇權 8
第四章 實驗數據 10
4.1 零息債券 10
4.2 歐式零息債券買權 13
4.3 美式零息債券賣權 16
第五章 結論 21
參考文獻 22

Cox, J., Ingersoll, J., & Ross, S. (1985). A Theory of the Term Structure of Interest Rates. Econometrica, 53(2), 385–407.
Dai, T., & Lyuu, Y. (2010). The Bino-Trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing. Journal of Derivatives, 17(4), 7–24.
Hilliard, J. E. (2014). Robust Binomial Lattices for Univariate and Multivariate Applications: Choosing Probabilities to Match Local Densities, Quantitative Finance, 14(1), 101–110.
Nawalkha, S. K., & Beliaeva, N. A. (2007). Efficient Trees for CIR and CEV Short Rate Models. Journal of Alternative Investments, 10(1), 71–90.
Nelson, D. B., & Ramaswamy, K. (1990). Simple Binomial Processes as Diffusion Approximations in Financial Models. Review of Financial Studies, 3(3), 393–430.
Zhang, Yu-Quan (2019). Pricing Multi-Asset Time-Varying Double-Barrier Options with Time-Dependent Parameters, Master’s thesis, Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan.