A primer on quasi-random numbers for copula models

In comparison to pseudo-random numbers, quasi-random numbers can significantly reduce sampling errors by filling the unit hypercube more uniformly. This property has enabled the corresponding quasi-Monte Carlo methods to improve upon classical Monte Carlo methods for many problems arising from a variety of stochastic models. The models for which this improvement has been seen mostly rely on independent margins or the multivariate normal distribution. The use of quasi-Monte Carlo methods on more general distributions remains mostly unexplored. The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Detailed examples (in the context of finance and insurance), illustrations and simulations are given and software has been developed and provided in the R packages copula and qrng.