  Efficiently pricing multi-asset options poses a significant challenge in
quantitative finance. The Monte Carlo (MC) method remains the prevalent choice
for pricing engines; however, its slow convergence rate impedes its practical
application. Fourier methods leverage the knowledge of the characteristic
function to accurately and rapidly value options with up to two assets.
Nevertheless, they face hurdles in the high-dimensional settings due to the
tensor product (TP) structure of commonly employed quadrature techniques. This
work advocates using the randomized quasi-MC (RQMC) quadrature to improve the
scalability of Fourier methods with high dimensions. The RQMC technique
benefits from the smoothness of the integrand and alleviates the curse of
dimensionality while providing practical error estimates. Nonetheless, the
applicability of RQMC on the unbounded domain, $\mathbb{R}^d$, requires a
domain transformation to $[0,1]^d$, which may result in singularities of the
transformed integrand at the corners of the hypercube, and deteriorate the rate
of convergence of RQMC. To circumvent this difficulty, we design an efficient
domain transformation procedure based on the derived boundary growth conditions
of the integrand. This transformation preserves the sufficient regularity of
the integrand and hence improves the rate of convergence of RQMC. To validate
this analysis, we demonstrate the efficiency of employing RQMC with an
appropriate transformation to evaluate options in the Fourier space for various
pricing models, payoffs, and dimensions. Finally, we highlight the
computational advantage of applying RQMC over MC or TP in the Fourier domain,
and over MC in the physical domain for options with up to 15 assets.
