The Term Structure of Interest Rate Differentials in a Target Zone: Theory and Swedish Data
Lars E.O. Svensson
The term structure of interest rate differentials is derived in a model of a small open
economy with a target zone exchange rate regime. The target zone is modeled as a
regulated Brownian motion. The interest rate differentials are computed as the solution
to a parabolic partial differential equation with derivative boundary conditions, both via a
Fourier-eries analytical solution and via a direct numerical solution. Several specific
properties of the term structure of interest rate differentials are derived. For instance, for
given time to maturity the interest rate differential is decreasing in the exchange rate, and
for given exchange rate the interest rate differential's absolute value and its instantaneous
variability are both decreasing in the time to maturity. Devaluation/realignment risks
are incorporated and imply upward shifts of the interest rate differentials. Some
implications of the theory are found to be broadly consistent with data on Swedish
exchange rates and interest differentials for the period 1986-1989.
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