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Dependence Modeling

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Cost-efficiency in multivariate Lévy models

Ludger Rüschendorf
  • Department of Mathematical Stochastics, University of Freiburg, Eckerstraße 1, 79104 Freiburg, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Viktor Wolf
  • Department of Mathematical Stochastics, University of Freiburg, Eckerstraße 1, 79104 Freiburg, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-04-16 | DOI: https://doi.org/10.1515/demo-2015-0001

Abstract

In this paper we determine lowest cost strategies for given payoff distributions called cost-efficient strategies in multivariate exponential Lévy models where the pricing is based on the multivariate Esscher martingale measure. This multivariate framework allows to deal with dependent price processes as arising in typical applications. Dependence of the components of the Lévy Process implies an influence even on the pricing of efficient versions of univariate payoffs.We state various relevant existence and uniqueness results for the Esscher parameter and determine cost efficient strategies in particular in the case of price processes driven by multivariate NIG- and VG-processes. From a monotonicity characterization of efficient payoffs we obtain that basket options are generally inefficient in Lévy markets when pricing is based on the Esscher measure.We determine efficient versions of the basket options in real market data and show that the proposed cost efficient strategies are also feasible from a numerical viewpoint. As a result we find that a considerable efficiency loss may arise when using the inefficient payoffs.

Keywords: cost-efficient strategies; multivariate Lévy models; multivariate Esscher transform; basket option

AMS:: 91B24; 60G51; 91B16

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About the article


Received: 2014-11-05

Accepted: 2015-04-06

Published Online: 2015-04-16


Citation Information: Dependence Modeling, Volume 3, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2015-0001.

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© 2015 Ludger Rüschendorf and Viktor Wolf. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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