Martingale transport with homogeneous stock movements

TL;DR

This paper introduces a time-homogeneity assumption into the multi-period martingale optimal transport problem to derive more robust and consistent price bounds for financial derivatives, with practical implications demonstrated through numerical examples.

Contribution

It proposes a novel time-homogeneity constraint in martingale transport, enhancing the integration of multi-time market data for derivative pricing.

Findings

Time-homogeneity improves price bounds accuracy.

The approach incorporates multi-time market data effectively.

Numerical examples demonstrate practical applicability.

Abstract

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.