  We develop an exchange rate target zone model with finite exit time and
non-Gaussian tails. We show how the tails are a consequence of time-varying
investor risk aversion, which generates mean-preserving spreads in the
fundamental distribution. We solve explicitly for stationary and non-stationary
exchange rate paths, and show how both depend continuously on the distance to
the exit time and the target zone bands. This enables us to show how central
bank intervention is endogenous to both the distance of the fundamental to the
band and the underlying risk. We discuss how the feasibility of the target zone
is shaped by the set horizon and the degree of underlying risk, and we
determine a minimum time at which the required parity can be reached. We prove
that increases in risk after a certain threshold can yield endogenous regime
shifts where the ``honeymoon effects'' vanish and the target zone cannot be
feasibly maintained. None of these results can be obtained by means of the
standard Gaussian or affine models. Numerical simulations allow us to recover
all the exchange rate densities established in the target zone literature. The
generality of our framework has important policy implications for modern target
zone arrangements.
