  We consider the infinite dimensional Heston stochastic volatility model
proposed in \arXiv:1706:03500. The price of a forward contract on a
non-storable commodity is modelled by a generalized Ornstein-Uhlenbeck process
in the Filipovi\'{c} space with this volatility. We prove different
representation formulas for the forward price. Then we consider prices of
options written on these forward contracts and we study sensitivity analysis
with computation of the Greeks with respect to different parameters in the
model. Since these parameters are infinite dimensional, we need to reinterpret
the meaning of the Greeks. For this we use infinite dimensional Malliavin
calculus and a randomization technique.
