  In this paper, we discuss the application of quasi-Monte Carlo methods to the
Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact
simulation scheme for the Heston model. As the joint transition densities are
not available in closed-form, the Linear Transformation method due to Imai and
Tan, a popular and widely applicable method to improve the effectiveness of
quasi-Monte Carlo methods, cannot be employed in the context of path-dependent
options when the underlying price process follows the Heston model.
Consequently, we tailor quasi-Monte Carlo methods directly to the Heston model.
The contributions of the paper are threefold: We firstly show how to apply
quasi-Monte Carlo methods in the context of the Heston model and the SVJ model,
secondly that quasi-Monte Carlo methods improve on Monte Carlo methods, and
thirdly how to improve the effectiveness of quasi-Monte Carlo methods by using
bridge constructions tailored to the Heston and SVJ models. Finally, we provide
some extensions for computing greeks, barrier options, multidimensional and
multi-asset pricing, and the 3/2 model.
