The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by
Is there a similar (in the sense that it depends on the marginal densities) upper bound for the copula density $c(u_1,…,u_d)$ instead of the CDF?
Any reference would be greatly appreciated.
Generally speaking, no there isn’t. For example, in the bivariate gaussian copula case, the quantity in the exponent has a saddle point at (0,0), and therefore explodes to infinity in two directions.
If you come across a class of copula densities that are in fact bounded, please let me know!