國立臺灣大學財務金融系Chien, Hsin-HuanHsin-HuanChien2006-09-272018-07-092006-09-272018-07-092003-06http://ntur.lib.ntu.edu.tw//handle/246246/20060927122847601268The purpose of this thesis is to illustrate how the lattice of the RS algorithm grows with the number of time periods under the proportional RS model with a flat forward rate curve. Our finding is that the RS algorithm grows exponentially under particular assumptions for small time partition ¢t, or, equivalently, large n. In the paper of Cakici & Zhu (2001), the algorithm based on the RS algorithm is simplified without “mean tracking.” We mean that the tree’s growth is centered around its mean. The thesis shows how their algorithm explodes exponentially too. After showing the growth rate of the lattice by the mathematical approach, this thesis will provide numerical examples on the RS algorithm & compare the numerical results with our theoretical results. The numerical results confirm the theoretical results that the lattice explodes exponentially for su±ciently large n. For example, under parameters ¾ = 0:25, T = 5, · = 0:02, & r0 = 0:04 (to be defined later), the algorithm works fine for about n · 310. Once n is larger, the total number of nodes will grow exponentially large beyond computer memory capacity.application/pdf268040 bytesapplication/pdfzh-TWreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/20060927122847601268/1/thesis_r90723063.pdf