2014/08/06 by Olena Burkovska, Burkovska, Olena, Bernard Haasdonk +5
Economics, Econometrics and Finance · #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1408.1220
openalex publication_date 2014/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we present a reduced basis method for pricing European and\nAmerican options based on the Black-Scholes and Heston model. To tackle each\nmodel numerically, we formulate the problem in terms of a time dependent\nvariational equality or inequality. We apply a suitable reduced basis approach\nfor both types of options. The characteristic ingredients used in the method\nare a combined POD-Greedy and Angle-Greedy procedure for the construction of\nthe primal and dual reduced spaces. Analytically, we prove the reproduction\nproperty of the reduced scheme and derive a posteriori error estimators.\nNumerical examples are provided, illustrating the approximation quality and\nconvergence of our approach for the different option pricing models. Also, we\ninvestigate the reliability and effectivity of the error estimators.\n