On intermediate Marginals in Martingale Optimal Transportation

TL;DR

This paper investigates how incorporating intermediate marginal distributions, derived from call option prices at various maturities, affects the bounds in martingale optimal transport problems, with implications for model-independent pricing.

Contribution

It characterizes market conditions under which additional intermediate marginals improve or do not improve price bounds in martingale optimal transport.

Findings

Additional call option prices can significantly tighten price bounds.

Certain market configurations do not benefit from extra marginal information.

Numerous examples demonstrate the impact of intermediate marginals on pricing bounds.

Abstract

We study the influence of additional intermediate marginal distributions on the value of the martingale optimal transport problem. From a financial point of view, this corresponds to taking into account call option prices not only, as usual, for those call options where the respective future maturities coincide with the maturities of some exotic derivative but also additional maturities and then to study the effect on model-independent price bounds for the exotic derivative. We characterize market settings, i.e., combinations of the payoff of exotic derivatives, call option prices and marginal distributions that guarantee improved price bounds as well as those market settings that exclude any improvement. Eventually, we showcase in numerous examples that the consideration of additional price information on vanilla options may have a considerable impact on the resultant model-independent price bounds.