  We consider stochastic volatility models under parameter uncertainty and
investigate how model derived prices of European options are affected. We let
the pricing parameters evolve dynamically in time within a specified region,
and formalise the problem as a control problem where the control acts on the
parameters to maximise/minimise the option value. Through a dual representation
with backward stochastic differential equations, we obtain explicit equations
for Heston's model and investigate several numerical solutions thereof. In an
empirical study, we apply our results to market data from the S&P 500 index
where the model is estimated to historical asset prices. We find that the
conservative model-prices cover 98% of the considered market-prices for a set
of European call options.
