The standard Gaussian copula model, with its overlay of base correlation, is useful but not ideal. It is essentially a static look-up table that does not model the dynamics of the process. It is hard to extend to bespoke baskets or other products, and it readily admits arbitrage.
Various models have been proposed to address these problems. These include both structural models that drive the value of the firm (or proxy) and reduced-form models that drive default intensity rates or the loss distri