The Reduced Basis Method for Option Pricing
International Internship Thesis
Supervision
Description
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.
Keywords
reduced basis method, option pricing, proper orthogonal decomposition
References:
- Y. Achdou and O. Pironneau,
Numerical Methods for Option Pricing,
SIAM, Philadelphia, USA, 2005.
- M. Avellaneda, D. Boyen-Olson, J. Busca and P. Fritz,
Reconstructing volatility, Risk (2002), 91-95.
- B. Dupire,
Pricing with a smile, Risk 7 (1994), 18-20.
- 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.
- 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.
- O. Pironneau,
Calibration of Options on a Reduced Basis,
J. Comput. Appl. Math. 232 (2009), 139-147.
