Smooth Interpolation of Zero Curves
نویسنده
چکیده
Smoothness is a desirable characteristic of interpolated zero curves; not only is it intuitively appealing, but there is some evidence that it provides more accurate pricing of securities. This paper outlines the mathematics necessary to understand the smooth interpolation of zero curves, and describes two useful methods: cubic-spline interpolation—which guarantees the smoothest interpolation of continuously compounded zero rates—and smoothest forwardrate interpolation—which guarantees the smoothest interpolation of the continuously compounded instantaneous forward rates. Since the theory of spline interpolation is explained in many textbooks on numerical methods, this paper focuses on a careful explanation of smoothest forward-rate interpolation.
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