| Summary: | 碩士 === 國立臺灣大學 === 資訊工程研究所 === 85 ===
Interest-rate-contingent claims such as caps, swaptins, bonds options, captions and mortgate-backed securities have become increasingly popular in recent year. The valuation of these instruents is now a major concern for both practitioners and academics.
In one simple and versatile mode of interest rates, all security and rates depend on only one factor--the short rate. The current structure of long rates and their estimated volatilities are used to construct a tree of possible future short rates. This tree can then be used to value interest-rate-sensitive securities.
The main contibution of this thesis is a general approach to calibrate the tree of short rates efficiently. Two important concepts are introduced that can greatly speed up the process and save much space. They are the concepts of differential tree and forward induction. With them, the running time can be reduced to O(n2) and the space to O(n), where n is the number of time periods. The results are very encouraging. For example, interest rate trees with hundreds of periods can usually be calibrated within 20 seconds. Even trees with up to 2000 periods can constructed within 100 seconds.
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