Résumé (EN)

In this paper, we present a reduced basis method for pricing European and Amer-ican options based on the Black-Scholes and Heston model. To tackle each model numerically, weformulate the problem in terms of a time dependent variational equality or inequality. We applya suitable reduced basis approach for both types of options. The characteristic ingredients used inthe method are a combined POD-Greedy and Angle-Greedy procedure for the construction of theprimal and dual reduced spaces. Analytically, we prove the reproduction property of the reducedscheme and derive a posteriori error estimators. Numerical examples are provided, illustrating theapproximation quality and convergence of our approach for the di erent option pricing models. Also,we investigate the reliability and e ectivity of the error estimators.