CIR模型的三元樹方法

A Trinomial Tree for the CIR model

黃顯鈞(Hsien-Chun Huang)

指導教授 ： 呂育道

國立臺灣大學/電機資訊學院/資訊工程學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901770

摘要

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。

關鍵字

CIR 模型 ； 三元樹 ； 零息債券評價

並列摘要

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.

並列關鍵字

CIR model ； trinomial tree ； zero-coupon bond pricing

參考文獻

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.