  We study a variant of the martingale optimal transport problem in a
multi-period setting to derive robust price bounds of a financial derivative.
On top of marginal and martingale constraints, we introduce a time-homogeneity
assumption, which restricts the variability of the forward-looking transitions
of the martingale across time. We provide a dual formulation in terms of
superhedging and discuss relaxations of the time-homogeneity assumption by
adding market frictions. In financial terms, the introduced time-homogeneity
corresponds to a time-consistency condition for call prices, given the state of
the stock. The time homogeneity assumption leads to improved price bounds as
market data from many time points can be incorporated effectively. The approach
is illustrated with two numerical examples.
