Static Replication of European Standard Dispersion Options

The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan (1998), extends to "standard dispersion" options written on the Euclidean norm of a vector of n asset performances. With the help of fractional calculus techniques we derive replicating portfolios for calls, puts and indeed any claim contingent on standard dispersion using vanilla basket calls whose basket weights span an n-dimensional continuum. Consequently multi-asset standard dispersion options admit a "model-free" price enforced by arbitrage, just as single-asset European claims do.