  This paper presents a methodology to introduce time-dependent parameters for
a wide family of models preserving their analytic tractability. This family
includes hybrid models with stochastic volatility, stochastic interest-rates,
jumps and their non-hybrid counterparts. The methodology is applied to Heston's
model. A bootstrapping algorithm is presented for calibration. A case study
works out the calibration of the time-dependent parameters to the volatility
surface of the Eurostoxx 50 index. The methodology is also applied to the
analytic valuation of forward start vanilla options driven by Heston's model.
This result is used to explore the forward skew of the case study.
