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

Journal Article · Thu Aug 01 00:00:00 EDT 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-013-9197-1· OSTI ID:22122871

Bonnans, J. Frederic, E-mail: [e-mail] ^[1]; Tan Xiaolu, E-mail: [e-mail] ^[2]

---

1. Ecole Polytechnique, INRIA-Saclay (France)
2. Ecole Polytechnique, CMAP (France)

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.

• OSTI ID: 22122871
• Journal Information: Applied Mathematics and Optimization, Vol. 68, 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); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
APPROXIMATIONS
CONVERGENCE
DISTRIBUTION
EFFICIENCY
OPTIMIZATION
VARIATIONAL METHODS