A Market Test for the Positivity of Arrow-Debreu Prices

TITLE: A Market Test for the Positivity of Arrow-Debreu Prices.

AUTHORS: Alexandre d'Aspremont

ABSTRACT: We derive tractable necessary and sufficient conditions for the absence of buy-and-hold arbitrage opportunities in a perfectly liquid, one period market. We formulate the positivity of Arrow-Debreu prices as a generalized moment problem to show that this no arbitrage condition is equivalent to the positive semidefiniteness of matrices formed by the market price of tradeable securities and their products. We apply this result to a market with multiple assets and basket call options.

STATUS: Frontiers in Quantitative Finance: Credit Risk and Volatility Modeling, Wiley, November 2008.

ArXiv PREPRINT: cs.CE/0510027

PAPER: Local pdf file