  We study indifference pricing of exotic derivatives by using hedging
strategies that take static positions in quoted derivatives but trade the
underlying and cash dynamically over time. We use real quotes that come with
bid-ask spreads and finite quantities. Galerkin method and integration
quadratures are used to approximate the hedging problem by a finite dimensional
convex optimization problem which is solved by an interior point method. The
techniques are extended also to situations where the underlying is subject to
bid-ask spreads. As an illustration, we compute indifference prices of
path-dependent options written on S&P500 index. Semi-static hedging improves
considerably on the purely static options strategy as well as dynamic trading
without options. The indifference prices make good economic sense even in the
presence of arbitrage opportunities that are found when the underlying is
assumed perfectly liquid. When transaction costs are introduced, the arbitrage
opportunities vanish but the indifference prices remain almost unchanged.
