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 \mbox{%DIFAUXCMD BeiglJuil0pt%DIFAUXCMD , following the construction of \mbox{%DIFAUXCMD BrenierMartingale}0pt%DIFAUXCMD , }  as well as the one 0pt%DIFAUXCMD and further studied in \mbox{%DIFAUXCMD BrenierMartingale}\hspace{0pt}%DIFAUXCMD . We show that, } in \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013}\hspace{0pt}%DIFAUXCMD , 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 \mbox{%DIFAUXCMD \cite{BrenierMartingale}\hspace{0pt}%DIFAUXCMD 's construction, the change of numeraire can be viewed as a mirror coupling for positive martingales, while for \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013} }\hspace{0pt}%DIFAUXCMD it }  }\hspace{0pt}%DIFAUXCMD } 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}\hspace{0pt}%DIFAUXCMD 's construction, the right monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire. An application to stochastic volatility models is also } provided.
In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan 0pt%DIFAUXCMD , following the construction of \mbox{%DIFAUXCMD BrenierMartingale}0pt%DIFAUXCMD , } constructed in \mbox{%DIFAUXCMD HobsonKlimmek2013 as well as the one introduced in \mbox{%DIFAUXCMD BeiglJuil0pt%DIFAUXCMD and further studied in \mbox{%DIFAUXCMD BrenierMartingale}\hspace{0pt}%DIFAUXCMD . We show that, } in }\hspace{0pt}%DIFAUXCMD , to } the case of positive martingales , a suitable change of numeraire }\hspace{0pt}%DIFAUXCMD 's construction, the change of numeraire can be viewed as a mirror coupling for positive martingales, while for \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013} }\hspace{0pt}%DIFAUXCMD it } applied to \mbox{%DIFAUXCMD \cite{HobsonKlimmek2013 }\hspace{0pt}%DIFAUXCMD } exchanges forward start straddles of type I and type II , so that the optimal transport plan in the subhedging problems is the same for both types of options. Moreover, for \mbox{%DIFAUXCMD \cite{BrenierMartingale}\hspace{0pt}%DIFAUXCMD 's construction, the right monotone transference plan can be viewed as a mirror coupling of its left counterpart under the change of numeraire. An application to stochastic volatility models is also } provided.
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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
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on the corresponding super and subhedging model-free prices. It turns out that, for \mbox{%DIFAUXCMD \cite{BrenierMartingale
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Some numerical applications are
Moreover, for \mbox{%DIFAUXCMD \cite{BrenierMartingale