Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis


The Reduced Basis Method for Option Pricing

International Internship Thesis



In this thesis we want to investigate a reduced basis approach (as pioneered by Maday, Patera and Turinici in the context of fluid dynamics) with a convex combination of the basis functions to an option pricing problem.


reduced basis method, option pricing, proper orthogonal decomposition


  1. Y. Achdou and O. Pironneau, Numerical Methods for Option Pricing, SIAM, Philadelphia, USA, 2005.
  2. M. Avellaneda, D. Boyen-Olson, J. Busca and P. Fritz, Reconstructing volatility, Risk (2002), 91-95.
  3. B. Dupire, Pricing with a smile, Risk 7 (1994), 18-20.
  4. M. Grepl and A.T. Patera A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations, ESAIM: Mathematical Modelling and Numerical Analysis 39 (2005), 157-181.
  5. Y. Maday, A.T. Patera and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations, J. Sci. Comput. 17 (2002), 437-446.
  6. O. Pironneau, Calibration of Options on a Reduced Basis, J. Comput. Appl. Math. 232 (2009), 139-147.

University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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