In Aladdin's Monte Carlo VaR, the default setting for the joint distribution of factor returns is multivariate normal. Given that normal distributions do not capture the fat tails seen in empirical financial returns, what is the advantage of running a Monte Carlo VaR vs. a parametric approach?
Monte Carlo VaR is good for portfolios that have instruments with non-linear payoffs, such as options and positions with embedded options (mortgage back securities, convertible bonds, etc.) It is also good for positions that have path dependency. Parametric VaR is difficult to use for these instruments in that the distribution of returns assumptions do not hold (namely normally distributed returns around an expected return). Monte Carlo VaR will produce a simulated path of returns on an underlying and reprice the non-linear and path dependent positions based on a simulated path of returns. The pricing and returns generated from those prices are then used to provide a VaR for a portfolio that contains such instruments.
Apparently that is just a limitation of Aladdin.
There is nothing to prevent you from computing VaR (as a percentile of the portfolio return distribution) using a better stochastic model for the factors that can incorporate fat tails, etc. Copula models can be used to introduce non-normality of the joint distribution (tail dependency) even if marginal distributions are normal.
In fact, much of this non-normal behavior would be difficult if not impossible to capture in a parametric approach with a closed-form solution.