Super-replication in Fully Incomplete Markets

TL;DR

This paper introduces fully incomplete markets where super-replication prices are model-independent, demonstrating their equivalence to model-free prices, with examples in stochastic and rough volatility models.

Contribution

It defines fully incomplete markets and proves super-replication prices are unaffected by model knowledge, providing new classes of such markets and computational examples.

Findings

Super-replication prices equal model-free prices in fully incomplete markets

Fully incomplete markets include stochastic and rough volatility models

Computational examples illustrate the theoretical results

Abstract

In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide 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.