On the Complexity of the Ritchken Sankarasubramanian Interest Rate Model
Date Issued
2003-06
Date
2003-06
Author(s)
Chien, Hsin-Huan
DOI
20060927122847601268
Abstract
The 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.
Publisher
臺北市:國立臺灣大學財務金融系
Type
report
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