Static Replication of European Multi-Asset Options with Homogeneous Payoff
12 Pages Posted: 28 Apr 2021
Date Written: April 27, 2021
Abstract
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: Suggested Citation