Detection of Arbitrage in a Market with Multi-Asset Derivatives and Known Risk-Neutral Marginals

Posted: 26 Jul 2012 Last revised: 9 Dec 2017

Multiple version iconThere are 2 versions of this paper

Date Written: April 1, 2015

Abstract

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 results about improved Fréchet-Hoeffding bounds in presence of additional information. For both methods, details of implementation steps and empirical applications are provided.

Keywords: Multi-Asset Derivative; Arbitrage; Incomplete Market; Risk-Neutral Measure; Multivariate Distribution; Copula Function

JEL Classification: G10, C52, D81

Suggested Citation

Tavin, Bertrand, Detection of Arbitrage in a Market with Multi-Asset Derivatives and Known Risk-Neutral Marginals (April 1, 2015). Journal of Banking and Finance, Volume 53, April 2015, Pages 158-178, Available at SSRN: https://ssrn.com/abstract=2117004 or http://dx.doi.org/10.2139/ssrn.2117004

Bertrand Tavin (Contact Author)

emlyon business school ( email )

23 Avenue Guy de Collongue
Ecully, 69132
France

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