Assessing alternative multivariate domain transformations for RQMC Fourier pricing

Investigate the efficiency of using the Rosenblatt transformation, the Nataf transformation, or copula-based constructions to handle the multivariate inverse cumulative distribution function within the domain transformation required for applying randomized quasi–Monte Carlo in the Fourier option pricing framework for multi-asset models, in comparison to the current linear-transform approach based on Cholesky/eigendecomposition.

Background

The paper proposes a model-specific domain transformation to enable randomized quasi–Monte Carlo (RQMC) integration on [0,1]^d for high-dimensional Fourier pricing. In the dependent-asset case, the authors avoid evaluating a multivariate inverse CDF by expressing the target distribution via normal mixtures and removing dependence through Cholesky or eigenvalue decompositions.

They note that other multivariate transformations—such as the Rosenblatt transformation, the Nataf transformation, or copula-based approaches—could also be used to address the multivariate ICDF step. However, the computational and convergence efficiency of these alternatives within the proposed RQMC-in-Fourier framework has not been evaluated.

Consequently, determining whether these alternative transformations improve or degrade performance relative to the linear-transform approach is explicitly deferred, forming an open task for future work.