  We determine the variance-optimal hedge when the logarithm of the underlying
price follows a process with stationary independent increments in discrete or
continuous time. Although the general solution to this problem is known as
backward recursion or backward stochastic differential equation, we show that
for this class of processes the optimal endowment and strategy can be expressed
more explicitly. The corresponding formulas involve the moment, respectively,
cumulant generating function of the underlying process and a Laplace- or
Fourier-type representation of the contingent claim. An example illustrates
that our formulas are fast and easy to evaluate numerically.
