Static Replication of European Multi-Asset Options with Homogeneous Payoff

12 Pages Posted: 28 Apr 2021

See all articles by Sebastien Bossu

Sebastien Bossu

NYU Courant; WPI Business School

Date Written: April 27, 2021


The replication of any European contingent claim by a static continuous portfolio of calls and puts, formally proven by Carr and Madan (1998), extends to multi-asset claims with absolutely homogeneous payoff. Using sophisticated tools from integral geometry, we show how such claims may be replicated with a continuum of vanilla basket calls and derive closed-form solutions to replicate two-asset best-of and worst-of options. We also derive a novel mathematical formula to invert the Radon transform which we apply to obtain a tractable expression of the joint implied distribution. Consequently, a large class of multi-asset options admit a model-free price enforced by arbitrage, just as single-asset European claims do.

Keywords: option replication, Breeden-Litzenberger, Radon transform, worst-of, best-of, exotic option, multi-asset, integral equation

JEL Classification: G12, G13, C60, C02

Suggested Citation

Bossu, Sebastien, Static Replication of European Multi-Asset Options with Homogeneous Payoff (April 27, 2021). Available at SSRN: or

Sebastien Bossu (Contact Author)

NYU Courant ( email )

251 Mercer Street
New York, NY - 10012
United States

WPI Business School ( email )

100 Institute Road
Worcester, MA 01609-2280
United States

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