  A parsimonious generalization of the Heston model is proposed where the
volatility-of-volatility is assumed to be stochastic. We follow the
perturbation technique of Fouque et al (2011, CUP) to derive a first order
approximation of the price of options on a stock and its volatility index. This
approximation is given by Heston's quasi-closed formula and some of its Greeks.
It can be very efficiently calculated since it requires to compute only Fourier
integrals and the solution of simple ODE systems. We exemplify the calibration
of the model with S&P 500 and VIX data.
