Static Replication of European Multi-Asset Options with Homogeneous Payoff

Abstract

ABSTRACT The replication of any European contingent claim by a static continuous portfolio of calls and puts, formally proven by [Carr, Peter, and Dilip Madan. 1998. “Towards a Theory of Volatility Trading.” In Volatility: New Estimation Techniques for Pricing Derivatives, Vol. 29, edited by Robert A. Jarrow, 417–427. Risk books.] 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.