Detection of Arbitrage in a Market with Multi-Asset Derivatives and Known Risk-Neutral Marginals
Université Paris 1 - Panthéon Sorbonne
November 6, 2012
Paris December 2012 Finance Meeting EUROFIDAI-AFFI Paper
In this paper we study the existence of arbitrage opportunities in a multi-asset market when risk-neutral marginal distributions of asset prices are known. We first propose an intuitive characterization of the absence of arbitrage opportunities in terms of copula functions. We then address the problem of detecting the presence of arbitrage by formalizing its resolution in two distinct ways that are both suitable for the use of optimization algorithms. The first method is valid in the general multivariate case and is based on Bernstein copulas that are dense in the set of all copula functions. The second one is easier to work with but is only valid in the bivariate case. It relies on recent results about improved Fréchet-Hoeffding bounds in presence of additional information. For both methods, details of implementation steps and empirical applications are provided.
Number of Pages in PDF File: 29
Keywords: Arbitrage, Multi-Asset Derivative, Incomplete Market, Risk-Neutral Measure, Multivariate Distribution, Copula Function
JEL Classification: G10, C52, D81working papers series
Date posted: June 9, 2012 ; Last revised: November 7, 2012
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