  We propose a new, data-driven approach for efficient pricing of - fixed- and
float-strike - discrete arithmetic Asian and Lookback options when the
underlying process is driven by the Heston model dynamics. The method proposed
in this article constitutes an extension of our previous work, where the
problem of sampling from time-integrated stochastic bridges was addressed. The
model relies on the Seven-League scheme, where artificial neural networks are
employed to "learn" the distribution of the random variable of interest
utilizing stochastic collocation points. The method results in a robust
procedure for Monte Carlo pricing. Furthermore, semi-analytic formulae for
option pricing are provided in a simplified, yet general, framework. The model
guarantees high accuracy and a reduction of the computational time up to
thousands of times compared to classical Monte Carlo pricing schemes.
