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Title: A Model-Free No-arbitrage Price Bound for Variance Options

We suggest a numerical approximation for an optimization problem, motivated by its applications in finance to find the model-free no-arbitrage bound of variance options given the marginal distributions of the underlying asset. A first approximation restricts the computation to a bounded domain. Then we propose a gradient projection algorithm together with the finite difference scheme to solve the optimization problem. We prove the general convergence, and derive some convergence rate estimates. Finally, we give some numerical examples to test the efficiency of the algorithm.
Authors:
 [1] ;  [2]
  1. Ecole Polytechnique, INRIA-Saclay (France)
  2. Ecole Polytechnique, CMAP (France)
Publication Date:
OSTI Identifier:
22122871
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 68; Journal Issue: 1; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; APPROXIMATIONS; CONVERGENCE; DISTRIBUTION; EFFICIENCY; OPTIMIZATION; VARIATIONAL METHODS