Static Replication of European Standard Dispersion Options
21 Pages Posted: 12 Oct 2020 Last revised: 6 Mar 2021
Date Written: February 28, 2021
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 integral equation 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.
Keywords: dispersion option, static replication, Radon transform, fractional integral equation, Carr-Madan formula, Breeden-Litzenberger formula
JEL Classification: G12, G13, C58, C02
Suggested Citation: Suggested Citation