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Cost-efficiency in multivariate Lévy models

Cost-efficiency in multivariate Lévy models AbstractIn this paper we determine lowest cost strategies for given payoff distributions called cost-efficientstrategies in multivariate exponential Lévy models where the pricing is based on the multivariate Esschermartingale measure. This multivariate framework allows to deal with dependent price processes as arisingin typical applications. Dependence of the components of the Lévy Process implies an influence even on thepricing of efficient versions of univariate payoffs.We state various relevant existence and uniqueness resultsfor the Esscher parameter and determine cost efficient strategies in particular in the case of price processesdriven by multivariate NIG- and VG-processes. From a monotonicity characterization of efficient payoffs weobtain that basket options are generally inefficient in Lévy markets when pricing is based on the Esschermeasure.We determine efficient versions of the basket options in real market data and show that the proposedcost efficient strategies are also feasible from a numerical viewpoint. As a result we find that a considerableefficiency loss may arise when using the inefficient payoffs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

Cost-efficiency in multivariate Lévy models

Dependence Modeling , Volume 3 (1): 1 – Apr 16, 2015

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Publisher
de Gruyter
Copyright
© 2015 Ludger Rüschendorf and Viktor Wolf
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2015-0001
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Dependence Modelingde Gruyter

Published: Apr 16, 2015

References