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A Note on ‘Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options’ by Tankov (2011)

Part of: Distribution theory - Probability Applications Mathematical finance

Published online by Cambridge University Press:  04 February 2016

Carole Bernard ,
Xiao Jiang  and
Steven Vanduffel
Carole Bernard*
Affiliation:
University of Waterloo
Xiao Jiang*
Affiliation:
University of Waterloo
Steven Vanduffel*
Affiliation:
Vrije Universiteit Brussel
*
∗ Postal address: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo ON, N2L 3G1, Canada.
∗ Postal address: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo ON, N2L 3G1, Canada.
∗∗∗∗ Postal address: Faculty of Economics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Elsene, Belgium. Email address: steven.vanduffel@vub.ac.be
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Abstract

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Tankov (2011) improved the Fréchet bounds for a bivariate copula when its values on a compact subset of [0, 1]2 are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be 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

CopulaFréchet-Hoeffding boundquasi-copulaoptimal portfolio selection

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62P05: Applications to actuarial sciences and financial mathematics 91G10: Portfolio theory
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 866 - 875
Copyright
© Applied Probability Trust 

References

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