  We consider assets for which price $X_t$ and squared volatility $Y_t$ are
jointly driven by Heston joint stochastic differential equations (SDEs). When
the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT},
Y_{nT})$, estimation errors do impact the classical option pricing PDEs. We
estimate these option pricing errors by combining numerical evaluation of
estimation errors for Heston SDEs parameters with the computation of option
price partial derivatives with respect to these SDEs parameters. This is
achieved by solving six parabolic PDEs with adequate boundary conditions. To
implement this approach, we also develop an estimator $\hat \lambda$ for the
market price of volatility risk, and we study the sensitivity of option pricing
to estimation errors affecting $\hat \lambda$. We illustrate this approach by
fitting Heston SDEs to 252 daily joint observations of the S\&P 500 index and
of its approximate volatility VIX, and by numerical applications to European
options written on the S\&P 500 index.
