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Pricing and hedging European options with discrete-time coherent risk

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Abstract

The aim of the paper is to provide as explicit as possible expressions for upper/lower prices and for superhedging/subhedging strategies based on discrete-time coherent risk measures. This is done on three levels of generality. For a general infinite-dimensional model, we prove the fundamental theorem of asset pricing. For a general multidimensional model, we provide expressions for prices and hedges. For a wide class of models, in particular, including GARCH, we give more concrete formulas, a sufficient condition for the uniqueness of a hedging strategy, and a numerical algorithm.

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Authors and Affiliations

  1. Department of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University, 119992, Moscow, Russia

    Alexander S. Cherny

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  1. Alexander S. Cherny
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Correspondence to Alexander S. Cherny.

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Cherny, A.S. Pricing and hedging European options with discrete-time coherent risk. Finance Stoch 11, 537–569 (2007). https://doi.org/10.1007/s00780-007-0050-8

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  • DOI: https://doi.org/10.1007/s00780-007-0050-8

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