Static Replication of European Standard Dispersion Options

21 Pages Posted: 12 Oct 2020 Last revised: 6 Mar 2021

See all articles by Sebastien Bossu

Sebastien Bossu

NYU Courant; WPI Business School

Peter Carr

New York University (NYU) - Finance and Risk Engineering Department

Andrew Papanicolaou

North Carolina State University - Department of Mathematics

Date Written: February 28, 2021

Abstract

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

Bossu, Sebastien and Carr, Peter and Papanicolaou, Andrew, Static Replication of European Standard Dispersion Options (February 28, 2021). Available at SSRN: https://ssrn.com/abstract=3705786 or http://dx.doi.org/10.2139/ssrn.3705786

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

HOME PAGE: http://https://www.wpi.edu/people/faculty/sbossu

Peter Carr

New York University (NYU) - Finance and Risk Engineering Department ( email )

6 Metrotech Center
New York, NY 11201
United States

Andrew Papanicolaou

North Carolina State University - Department of Mathematics ( email )

Campus Box 8205
NC State University
Raleigh, NC 27695-8205
United States

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