Before revision: We study the problem of super-replication of game options in general stochastic volatility models which include e. g. the Heston model, the Hull-White model and the Scott model. For simplicity, we consider models with one risky asset. We show that the super-replication price is the cheapest cost of a trivial super-replication strategy.
After revision: In this work we introduce the notion of extremely incomplete markets. We prove that for these markets the super-replication price is the cheapest cost of a trivial super-replication strategy.