  This paper analyses the implementation and calibration of the Heston
Stochastic Volatility Model. We first explain how characteristic functions can
be used to estimate option prices. Then we consider the implementation of the
Heston model, showing that relatively simple solutions can lead to fast and
accurate vanilla option prices. We also perform several calibration tests,
using both local and global optimization. Our analyses show that
straightforward setups deliver good calibration results. All calculations are
carried out in Matlab and numerical examples are included in the paper to
facilitate the understanding of mathematical concepts.
