Semi-static hedging under exchangeability type conditions

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 Lévy 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.