  In this paper we show that Hilbert space-valued stochastic models are robust
with respect to perturbation, due to measurement or approximation errors, in
the underlying volatility process. Within the class of stochastic volatility
modulated Ornstein-Uhlenbeck processes, we quantify the error induced by the
volatility in terms of perturbations in the parameters of the volatility
process. We moreover study the robustness of the volatility process itself with
respect to finite dimensional approximations of the driving compound Poisson
process and semigroup generator respectively, when considering operator-valued
Barndorff-Nielsen and Shephard stochastic volatility models. We also give
results on square root approximations. In all cases we provide explicit bounds
for the induced error in terms of the approximation of the underlying
parameter. We discuss some applications to robustness of prices of options on
forwards and volatility.
