Reduced Basis Methods for Pricing Options with the Black--Scholes and Heston Models
Burkovska, O.; Haasdonk, Bernard; Salomon, Julien; Wohlmuth, Barbara (2015), Reduced Basis Methods for Pricing Options with the Black--Scholes and Heston Models, SIAM Journal on Financial Mathematics, 6, 1, p. 685-712. 10.1137/140981216
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1408.1220v1
Journal nameSIAM Journal on Financial Mathematics
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Abstract (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.
Subjects / KeywordsHeston model; Black–Scholes model; Reduced basis method; Pricing options
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