  We derive an equation of motion for interest-rate yield curves by applying a
minimum Fisher information variational approach to the implied probability
density. By construction, solutions to the equation of motion recover observed
bond prices. More significantly, the form of the resulting equation explains
the success of the Nelson Siegel approach to fitting static yield curves and
the empirically observed modal structure of yield curves. A practical numerical
implementation of this equation of motion is found by using the Karhunen-Loeve
expansion and Galerkin's method to formulate a reduced-order model of yield
curve dynamics.
