NORTA for portfolio credit risk

We use NORTA (NORmal To Anything) to enhance normal credit-risk factor settings in modeling common risk factors and capturing contagion effects. NORTA extends the multivariate Normal distribution in that it enables the simulation of a random vector with arbitrary and known marginals and correlation structure. NORTA can be solved either by numerical integration (Cario and Nelson in Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix, Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, IL, 1997) or by Monte Carlo simulation (Ilich in Eur J Oper Res 192(2):468-478, 2009). The former approach, which is the most efficient, assumes that the marginals' inverse cumulative functions are given, while the latter, which is more flexible but less efficient, does not. We show how to combine both approaches for higher flexibility and efficiency. We solve for NORTA and experiment with Normal, Student, and Asymmetric Exponential Power (AEP) distributions. We match NORTA models to Normal models with the same marginals' first and second moments. Yet, differences in credit-risk measures can be highly significant. This supports NORTA as a viable alternative for credit-risk modeling and analysis.