Super-replication in fully incomplete markets

In this work, we introduce the notion of fully incomplete markets. We prove that for these markets, the super-replication price coincides with the model-free super-replication price. Namely, the knowledge of the model does not reduce the super-replication price. We provide two families of fully incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples. Our approach is purely probabilistic.