Pricing and hedging European options with discrete-time coherent risk |
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Authors: | Alexander S. Cherny |
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Affiliation: | (1) Department of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University, 119992 Moscow, Russia |
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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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Keywords: | Dynamic coherent risk measure Dynamic tail VaR Dynamic weighted VaR Fundamental theorem of asset pricing Hedging cash flow streams No good deals Price contribution Pricing cash flow streams Risk management Risk measurement |
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