| Summary: | 碩士 === 國立臺灣大學 === 資訊工程學系 === 86 === This thesis contains two main parts. In the first part, we
implement a new approach for constructing no-arbitrage models of
the term structure in terms of the process followed by the short
rate, r. The approach, which makes use of trinomial trees, is
relatively simple and computationally more efficient than
previous procedures. The procedure is appropriate for models
where there is some function x of the short rate r that follows a
mean-reverting arithmetic process. The key element of the
procedure is that it produces a tree that is symmetrical about the
expected value of x. A forward induction procedure is used to find
the positions of the central nodes at the end of each time step.
In the second part, the new tree-building procedure is extended to
model the yield curves in two different economies
simultaneously. We focus on the adjusted short rate trees, which
are constructed from the viewpoint of a risk-neutral investor
in the economy in which the cash flows are realized. We then
increase the number of economies and discuss arbitrage pricing therein.
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