Variance-optimal hedging for processes with stationary independent increments

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 back-ward 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 formula-,; 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.