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

J. Frederic Bonnans 1, 2 Xiaolu Tan 2
1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
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.
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J. Frederic Bonnans, Xiaolu Tan. A model-free no-arbitrage price bound for variance options. Applied Mathematics and Optimization, Springer Verlag (Germany), 2013, 68 (1), pp.43-73. ⟨10.1007/s00245-013-9197-1⟩. ⟨inria-00634387⟩

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