This thesis presents results of applying a variance reduction technique during the numerical solution of stochastic differential equations by Monte Carlo simulation. The problems of application are from the field of mathematical finance, specifically investigating both single-factor and multi-factor models of the short rate of interest and solving for the term structure of interest rates. The term structure is a weak solution of the short rate stochastic differential equation. The variance reduction method employed is due to Milstein and involves a change of measure for the original short rate equation. To substantially reduce the variance of the functional, the measure transformation method requires that a "good" guess of the solution to the corresponding partial differential equation for the weak solution be able to be made at every point along a simulated interest rate path.; The analysis of the variance reduction method applied to these term structure problems addresses three critical issues: the difference between the theoretical rate of convergence of a scheme and its actual rate of convergence calculated by regression analysis; the number of significant digits obtainable in the bond price after variance reduction assuming a minimum of paths is desirable to lower the execution time; and how "good" of a guess do you actually need to the true solution to impact the variance.
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