In this paper we consider the optimal transport approach for computing the model-free prices of a given path-dependent contingent claim in a two periods model. More precisely, we first revisit the optimal transport plan introduced in BeiglJuil, following the construction of BrenierMartingale, as well as the one in HobsonKlimmek2013 in the case of positive martingales and a single maximizer for the difference between the c.d.f.'s of the two marginals. These characterizations allow us to study the effect of the change of numeraire on the corresponding superhedging and subhedging model-free prices. It turns out that, for BrenierMartingale's construction, the change of numeraire can be viewed as a mirror coupling for positive martingales, while for HobsonKlimmek2013 it exchanges forward start straddles of type I and type II giving also that the optimal transport plan in the subhedging problems is the same for both types of options. Some numerical applications are provided.
In this paper we consider the optimal transport approach for computing the model-free prices of a given path-dependent contingent claim in a two periods model. More precisely, we first specialize the optimal transport plan introduced in BeiglJuil, following the construction of BrenierMartingale, as well as the one in HobsonKlimmek2013 , to the case of positive martingales and a single maximizer for the difference between the c.d.f.'s of the two marginals. These characterizations allow us to study the effect of the change of numeraire on the corresponding super and subhedging model-free prices. It turns out that, for BrenierMartingale's construction, the change of numeraire can be viewed as a mirror coupling for positive martingales, while for HobsonKlimmek2013 it exchanges forward start straddles of type I and type II giving also that the optimal transport plan in the subhedging problems is the same for both types of options. Some numerical applications are provided.
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