A reduced basis method for parabolic partial differential equations with parameter functions and application to option pricing

Antonia Mayerhofer and Karsten Urban

Journal of Computational Finance

Abstract: ABSTRACT We consider the Heston model as an example of a parameterized parabolic partial;differential equation. A space-time variational formulation is derived that allows for;parameters in the coefficients (for calibration) and enables us to choose the initial;condition (for option pricing) as a parameter function. A corresponding discretization;in space and time for the initial condition are introduced. Finally, we present a novel;reduced basis method that is able to use the initial condition of the parabolic partial;differential equation as a parameter (function). The corresponding numerical results;are shown.

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