Simulating from general copulas

[AlphaXi]

Hey guys,

Let say you want to simulate from a multivariate distribution on (\mathbb{R}^d) given by its copula and (d) margins. How would you proceed ? Is there any way to avoid the curse of dimensionality ? The case of most archimedean copulas can be treated using fast multivariate rejection sampling (cf this recent article). How about non-archimedean copulas ?

How fast are the usual methods ? As an example how long would take the computation of a classic basket option price on (d) assets ? Is it a real issue practically ?

Thanks!

 

[Tsotne]

In Archimedean copulas there are 3 main methods for simulation (best fitted for 2-3 dimensions) - see Roger Nelsen. As for non-Archimedean copulas you're going to encounter many problems as dimension increases both - from the point of analysis and practicality (in practicality I mean using Excel or some software handling simulations).