  Monte Carlo Approaches for calculating Value-at-Risk (VaR) are powerful tools
widely used by financial risk managers across the globe. However, they are time
consuming and sometimes inaccurate. In this paper, a fast and accurate Monte
Carlo algorithm for calculating VaR and ES based on Gaussian Mixture Models is
introduced. Gaussian Mixture Models are able to cluster input data with respect
to market's conditions and therefore no correlation matrices are needed for
risk computation. Sampling from each cluster with respect to their weights and
then calculating the volatility-adjusted stock returns leads to possible
scenarios for prices of assets. Our results on a sample of US stocks show that
the Gmm-based VaR model is computationally efficient and accurate. From a
managerial perspective, our model can efficiently mimic the turbulent behavior
of the market. As a result, our VaR measures before, during and after crisis
periods realistically reflect the highly non-normal behavior and non-linear
correlation structure of the market.
