A Harmonic Analysis Solution to the Static Basket Arbitrage Problem

15 Pages Posted: 13 Jul 2004

See all articles by Alexandre d'Aspremont

Alexandre d'Aspremont

Princeton University - Department of Operations Research and Financial Engineering

Date Written: September 2, 2003

Abstract

We consider the problem of computing upper and lower bounds on the price of a European basket call option, given prices on other similar baskets. We focus here on an interpretation of this program as a generalized moment problem. Recent results by Berg & Maserick (1984), Putinar & Vasilescu (1999) and Lasserre (2001) on harmonic analysis on semigroups, the K-moment problem and its applications to optimization, allow us to derive tractable necessary and sufficient conditions for the absence of static arbitrage between basket straddles, hence between basket calls and puts.

Keywords: Basket options, semidefinite programming, static arbitrage, K-moment

JEL Classification: C61, C63, G12

Suggested Citation

d'Aspremont, Alexandre, A Harmonic Analysis Solution to the Static Basket Arbitrage Problem (September 2, 2003). Available at SSRN: https://ssrn.com/abstract=563523 or http://dx.doi.org/10.2139/ssrn.563523

Alexandre D'Aspremont (Contact Author)

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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