University of Vienna

Robust pricing of an exotic derivative with payoff $\Phi$ can be viewed as the task of estimating its expectation $E_Q \Phi$ with respect to a martingale measure $Q$ satisfying marginal constraints. It has proven fruitful to relate this to the theory of Monge-Kantorovich optimal transport. For instance, the duality theorem from optimal transport leads to new super-replication results. Optimality criteria from the theory of mass transport can be translated to the martingale setup and allow to characterize minimizing/maximizing models in the robust pricing problem. Moreover, the dual viewpoint provides new insights to the classical inequalities of Doob and Burkholder-Davis-Gundy.

Based on ideas from rough path analysis and operator splitting, the Kusuoka-Lyons-Victoir scheme provides a family of higher order methods for the weak approximation of stochastic differential equations. Out of this family, the Ninomiya-Victoir method is especially simple to implement and to adjust to various different models. We give some examples of models used in financial engineering and comment on the performance of the Ninomiya-Victoir scheme and some modifications when applied to these models.