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Advanced Modelling in Mathematical Finance pp 331–377Cite as

Construction and Hedging of Optimal Payoffs in Lévy Models

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 189))

Abstract

The construction of lowest cost strategies for a given payoff has found considerable interest in recent literature and it has been shown in applications to real market data, that cost savings associated with these cost-efficient strategies can be quite substantial. In this paper we provide for a variety of options in the frame of Lévy models cost-efficient counterparts and determine the efficiency loss (resp. gain) in applications to several sets of market data. We discuss specific effects of the cost-efficient payoffs for a series of standard options like puts, calls, self-quanto puts and straddles and butterfly spread options, and develop their pricing. We obtain several new results on dependence of the magnitude of the efficiency loss on various model and option parameters. We show that the cost-efficient payoffs behave improved compared to the standard payoffs concerning hedging properties. We provide concrete hedging simulation schemes for various cost-efficient options. The results of the paper show that cost-efficient payoffs may lead to considerable reduction of cost in markets with pronounced trend.

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Author information

Authors and Affiliations

  1. Department of Mathematical Stochastics, University of Freiburg, Eckerstraße 1, 79104, Freiburg, Germany

    Ludger Rüschendorf & Viktor Wolf

Authors
  1. Ludger Rüschendorf
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  2. Viktor Wolf
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Correspondence to Ludger Rüschendorf .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Christian-Albrechts-Universität zu Kiel, Kiel, Germany

    Jan Kallsen

  2. Institute of Mathematics, Technische Universität Berlin, Berlin, Germany

    Antonis Papapantoleon

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Rüschendorf, L., Wolf, V. (2016). Construction and Hedging of Optimal Payoffs in Lévy Models. In: Kallsen, J., Papapantoleon, A. (eds) Advanced Modelling in Mathematical Finance. Springer Proceedings in Mathematics & Statistics, vol 189. Springer, Cham. https://doi.org/10.1007/978-3-319-45875-5_16

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