Robust Bounds for Derivative Prices in Markovian Models

Abstract

We study the optimal martingale transport problem under an additional constraint imposing the underlying process to be Markovian. This formulation results in a modified transportation problem in which the solutions correspond to robust price bounds for exotic derivatives within the class of calibrated martingale models exhibiting the Markov property. We investigate the arising consequences which comprise a dual perspective of the transport problem in terms of liquid replication strategies. Eventually an empirical investigation illustrates the influence of the Markov property on robust price bounds for financial derivatives.

Keywords: Optimal Martingale Transport, Robust Pricing, Markov Property, Duality

JEL Classification: C61, G13