  A leveraged exchange traded fund (LETF) is an exchange traded fund that uses
financial derivatives to amplify the price changes of a basket of goods. In
this paper, we consider the robust hedging of European options on a LETF,
finding model-free bounds on the price of these options.
  To obtain an upper bound, we establish a new optimal solution to the
Skorokhod embedding problem (SEP) using methods introduced in
Beiglb\"ock-Cox-Huesmann. This stopping time can be represented as the hitting
time of some region by a Brownian motion, but unlike other solutions of e.g.
Root, this region is not unique. Much of this paper is dedicated to
characterising the choice of the embedding region that gives the required
optimality property. Notably, this appears to be the first solution to the SEP
where the solution is not uniquely characterised by its geometric structure,
and an additional condition is needed on the stopping region to guarantee that
it is the optimiser. An important part of determining the optimal region is
identifying the correct form of the dual solution, which has a financial
interpretation as a model-independent superhedging strategy.
