Quasi-random numbers for copula models

TL;DR

This paper explores how quasi-random numbers can be integrated into copula sampling algorithms, enhancing efficiency and applicability beyond traditional models, with practical implementations in R for finance and insurance.

Contribution

It demonstrates the adaptation of copula sampling methods to quasi-random numbers, including faster stochastic representations, and provides software tools for practical use.

Findings

Quasi-random numbers improve sampling efficiency in copula models.

New algorithms extend quasi-random sampling to complex copula models.

Software implementations facilitate practical adoption in finance and insurance.

Abstract

The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a one-to-one transformation), it is also shown that typically faster sampling methods (based on stochastic representations) can be used to improve upon classical Monte Carlo methods when pseudo-random number generators are replaced by quasi-random number generators. This opens the door to quasi-random numbers for models well beyond independent margins or the multivariate normal distribution. 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.