Journal of Computational Finance
ISSN:
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
A reduced basis method for parabolic partial differential equations with parameter functions and application to option pricing
Need to know
- A reduced Basis space-time variational approach for parametric parabolic partial differential equations having coefficient parameters and a variable initial condition is introduced.
- Feasibility and efficiency are demonstrated.
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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