A Functional Analysis Approach to Static Replication of European Options

23 Pages Posted: 1 Jul 2019

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: June 29, 2019

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), is part of the more general theory of integral equations. We apply spectral decomposition techniques to show that replication may also be achieved with a discrete portfolio of special options. We propose a numerical application for fast pricing of vanilla options that may be suitable for large option books or high frequency option trading, and we use a reflected Brownian motion model to show how pricing formulas for the special options may be obtained.

Keywords: derivatives, options, static replication, payoff, integral equations, functional analysis, spectral theorem, Breeden-Litzenberger

JEL Classification: G10, C60

Suggested Citation

Bossu, Sebastien and Carr, Peter and Papanicolaou, Andrew, A Functional Analysis Approach to Static Replication of European Options (June 29, 2019). Available at SSRN: https://ssrn.com/abstract=3412244 or http://dx.doi.org/10.2139/ssrn.3412244

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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