  It turns out that in the bivariate Black-Scholes economy Margrabe type
options exhibit symmetry properties leading to semi-static hedges of rather
general barrier options. Some of the results are extended to variants obtained
by means of Brownian subordination. In order to increase the liquidity of the
hedging instruments for certain currency options, the duality principle can be
applied to set up hedges in a foreign market by using only European vanilla
options sometimes along with a risk-less bond. Since the semi-static hedges in
the Black-Scholes economy are exact, closed form valuation formulas for certain
barrier options can be easily derived.
