  We propose a model to quantify the effect of parameter uncertainty on the
option price in the Heston model. More precisely, we present a
Hamilton-Jacobi-Bellman framework which allows us to evaluate best and worst
case scenarios under an uncertain market price of volatility risk. For the
numerical approximation the Hamilton--Jacobi--Bellman equation is reformulated
to enable the solution with a finite element method. A case study with
butterfly options exhibits how the dependence of Delta on the magnitude of the
uncertainty is nonlinear and highly varied across the parameter regime.
  Keywords: Uncertain market price, Volatility risk, Hamilton-Jacobi-Bellman
equation, Finite element method, Uncertainty quantification
