It turns out that a slightly generalised Margrabe formula exhibits symmetry properties leading to semi-static hedges of rather general options in the bivariate Black-Scholes economy . In order to increase the liquidity of the used hedging instruments for  currency options, the duality principle can be used to set up the 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, a closed form valuation formula of a certain weighted barrier swap-option can be easily derived.
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.
R
a slightly generalised Margrabe formula exhibits
in the bivariate Black-Scholes economy Margrabe type options exhibit
R
options in the bivariate Black-Scholes economy
barrier options. Some of the results are extended to variants obtained by means of Brownian subordination
D
used
A
certain
R
used
applied
D
the
D
a
R
formula of a certain weighted barrier swap-option
formulas for certain barrier options