  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) as well as
choosing the initial condition (for option pricing) as a parameter function. A
corresponding discretization in space and time amd initial condition is
introduced and shown to be stable. Finally, a Reduced Basis Method (RBM) is
introduced that is able to use parameter functions also for the initial
condition. Corresponding numerical results are shown.
