  Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and
hedging of complex financial derivatives. These problems are usually of high
dimensionality and discontinuities. The two factors may significantly
deteriorate the performance of the QMC method. This paper develops an
integrated method that overcomes the challenges of the high dimensionality and
discontinuities concurrently. For this purpose, a smoothing method is proposed
to remove the discontinuities for some typical functions arising from financial
engineering. To make the smoothing method applicable for more general
functions, a new path generation method is designed for simulating the paths of
the underlying assets such that the resulting function has the required form.
The new path generation method has an additional power to reduce the effective
dimension of the target function. Our proposed method caters for a large
variety of model specifications, including the Black-Scholes, exponential
normal inverse Gaussian L\'evy, and Heston models. Numerical experiments
dealing with these models show that in the QMC setting the proposed smoothing
method in combination with the new path generation method can lead to a
dramatic variance reduction for pricing exotic options with discontinuous
payoffs and for calculating options' Greeks. The investigation on the effective
dimension and the related characteristics explains the significant enhancement
of the combined procedure.
