A Market Test for the Positivity of Arrow-Debreu Prices
Alexandre d'Aspremont
TL;DR
This paper establishes a mathematical framework linking no-arbitrage conditions in liquid markets to positive semidefiniteness of certain matrices, providing a practical test for Arrow-Debreu price positivity.
Contribution
It introduces a novel characterization of no-arbitrage conditions via a generalized moment problem and positive semidefiniteness, applicable to markets with multiple assets and options.
Findings
Derived necessary and sufficient conditions for no arbitrage
Connected Arrow-Debreu prices to positive semidefinite matrices
Applied the framework to markets with multiple assets and options
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.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models · Complex Systems and Time Series Analysis