  In this paper we analyse financial implications of exchangeability and
similar properties of finite dimensional random vectors. We show how these
properties are reflected in prices of some basket options in view of the
well-known put-call symmetry property and the duality principle in option
pricing. A particular attention is devoted to the case of asset prices driven
by Levy processes. Based on this, concrete semi-static hedging techniques for
multi-asset barrier options, such as certain weighted barrier spread options,
weighted barrier swap options or weighted barrier quanto-swap options are
suggested.
