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



Author: Michael Schmutz

Source: https://arxiv.org/







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