Hedging of Game Options under Model Uncertainty in Discrete Time

TL;DR

This paper develops a framework for pricing game options under model uncertainty in discrete time, deriving dual representations that connect super-replication prices with supremums over specific martingale measures and Dynkin game values.

Contribution

It introduces a novel approach to model uncertainty in discrete time for game options, providing new dual formulas and extending results to American options.

Findings

Super-replication prices equal supremums over certain martingale measures.

Dual expressions derived for game options with upper semicontinuous payoffs.

Results extend to American options, offering new insights.

Abstract

We introduce a setup of model uncertainty in discrete time. In this setup we derive dual expressions for the super--replication prices of game options with upper semicontinuous payoffs. We show that the super--replication price is equal to the supremum over a special (non dominated) set of martingale measures, of the corresponding Dynkin games values. This type of results is also new for American options.