Note on 'Improved Frechet Bounds and Model-Free Pricing of Multi-Asset Options' by Tankov (2011)

12 Pages Posted: 13 Feb 2012 Last revised: 11 May 2012

Carole Bernard

Grenoble Ecole de Management

Xiao Jiang

University of Waterloo

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: February 11, 2012

Abstract

Tankov (2011) improves the Fréchet bounds for a bivariate copula when its values on a compact subset of the unit square are given. He shows that the best possible bounds are quasi-copulas and gives a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. Next, we show how this can be very useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.

Keywords: bounds, copulas, Frechet Hoeffding bounds, quasi-copula, optimal investment, state dependent constraints

Suggested Citation

Bernard, Carole and Jiang, Xiao and Vanduffel, Steven, Note on 'Improved Frechet Bounds and Model-Free Pricing of Multi-Asset Options' by Tankov (2011) (February 11, 2012). Journal of Applied Probability, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2003462 or http://dx.doi.org/10.2139/ssrn.2003462

Carole Bernard (Contact Author)

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Xiao Jiang

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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