Portfolio Value-at-Risk and Expected-Shortfall Using an Efficient Simulation Approach Based on Gaussian Mixture Model

Abstract

Abstract 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.