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. Furthermore, we calculate explicitly the super-replication price and the corresponding optimal hedge. The super-replication price can be seen as the game variant of a concave envelope . Our approach is purely probabilistic.
In this work we introduce the notion of extremely 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 extremely incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples . Our approach is purely probabilistic.
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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
In this work we introduce the notion of extremely incomplete markets. We prove that for these markets
R
is the cheapest cost of a trivial
coincide with the model free
R
strategy. Furthermore, we calculate explicitly the
price. Namely, the knowledge of the model does not reduce the
D
price and the corresponding optimal hedge. The super-replication
R
can be seen as the game variant of a concave envelope
. We provide two families of extremely incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples