A Harmonic Analysis Solution to the Static Basket Arbitrage Problem

D'Aspremont, Alexandre

doi:10.2139/ssrn.563523

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A Harmonic Analysis Solution to the Static Basket Arbitrage Problem

Alexandre D'Aspremont

Princeton University - Department of Operations Research and Financial Engineering

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.

Number of Pages in PDF File: 15

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

JEL Classification: C61, C63, G12

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Date posted: July 13, 2004

Suggested Citation

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

Contact Information

Alexandre D'Aspremont (Contact Author)

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

Princeton, NJ 08544
United States