Martingale transport with homogeneous stock movements

Abstract

We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds on 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 since market data from many time points can be incorporated effectively. The approach is illustrated with two numerical examples.