A model-free no-arbitrage price bound for variance options

J. Frederic Bonnans () and Xiaolu Tan
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J. Frederic Bonnans: Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems - CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Xiaolu Tan: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: In the framework of Galichon, Henry-Labordère and Touzi, we consider the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset. We first make some approximations which restrict the computation on a bounded domain. Then we propose a gradient projection algorithm together with a finite difference scheme to approximate the bound. The general convergence result is obtained. We also provide a numerical example on the variance swap option.

Keywords: Variance option; model-free price bound; gradient projection algorithm.; gradient projection algorithm (search for similar items in EconPapers)
Date: 2013-07-04
Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00634387v1
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Citations: View citations in EconPapers (9)

Published in Applied Mathematics and Optimization, 2013, 68 (1), pp.43-73. ⟨10.1007/s00245-013-9197-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:inria-00634387

DOI: 10.1007/s00245-013-9197-1

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