  In a financial market model, we consider the variance-optimal semi-static
hedging of a given contingent claim, a generalization of the classic
variance-optimal hedging. To obtain a tractable formula for the expected
squared hedging error and the optimal hedging strategy, we use a Fourier
approach in a general multidimensional semimartingale factor model. As a
special case, we recover existing results for variance-optimal hedging in
affine stochastic volatility models. We apply the theory to set up a
variance-optimal semi-static hedging strategy for a variance swap in both the
Heston and the 3/2-model, the latter of which is a non-affine stochastic
volatility model.
