Multivariate Extension of Put-Call Symmetry

Multivariate analogues of the put-call symmetry can be expressed as certain symmetry properties of basket options and options on the maximum of several assets with respect to some (or all) permutations of the weights and the strike. The so-called self-dual distributions satisfying these symmetry conditions are completely characterized and their properties explored. It is also shown how to relate some multivariate asymmetric distributions to symmetric ones by a power transformation that is useful to adjust for carrying costs. Particular attention is devoted to the case of asset prices driven by Levy processes. Based on this, semistatic hedging techniques for multiasset barrier options are suggested.