A Harmonic Analysis Solution to the Static Basket Arbitrage Problem

Details A Harmonic Analysis Solution to the Static Basket Arbitrage Problem A Harmonic Analysis Solution to the Static Basket Arbitrage Problem

2003-09-02

arxiv.org/abs/math/0309048v1

Mathematics

Optimization and Control

Preliminary version for IMA workshop "Risk Management and Model Specifications Issues in Finance". Numerical results to be add

Scientific paper

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.

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