A Functional Analysis Approach to Static Replication of European Options
23 Pages Posted: 1 Jul 2019
Date Written: June 29, 2019
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: Suggested Citation