Cost-efficiency in multivariate Lévy models

Ludger Rüschendorf; Viktor Wolf

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 1-16, electronic only
  • ISSN: 2300-2298

Abstract

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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.

How to cite

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Ludger Rüschendorf, and Viktor Wolf. "Cost-efficiency in multivariate Lévy models." Dependence Modeling 3.1 (2015): 1-16, electronic only. <http://eudml.org/doc/270841>.

@article{LudgerRüschendorf2015,
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.},
author = {Ludger Rüschendorf, Viktor Wolf},
journal = {Dependence Modeling},
keywords = {cost-efficient strategies; multivariate Lévy models; multivariate Esscher transform; basket option},
language = {eng},
number = {1},
pages = {1-16, electronic only},
title = {Cost-efficiency in multivariate Lévy models},
url = {http://eudml.org/doc/270841},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Ludger Rüschendorf
AU - Viktor Wolf
TI - Cost-efficiency in multivariate Lévy models
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 1
EP - 16, electronic only
AB - 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.
LA - eng
KW - cost-efficient strategies; multivariate Lévy models; multivariate Esscher transform; basket option
UR - http://eudml.org/doc/270841
ER -

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