Market risk measures using finite Gaussian mixtures

Value at Risk (VaR) is the most popular market risk measure as it summarizes in one figure the exposure to different risk factors. It had been around for over a decade when Expected Shortfall (ES) emerged to correct its shortcomings. Both risk measures can be estimated under several models. We explore the application of a parametric model to fit the joint distribution of risk factor returns based on multivariate finite Gaussian Mixtures, derive a closed-form expression for ES under this model and estimate risk measures for a multi-asset portfolio over an extended period. We then compare results versus benchmark models (Historical Simulation and Normal) through back-testing all of them at several confidence levels. Evidence shows that the proposed model is a competitive one for the estimation of VaR and ES.
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Market risk measures using finite Gaussian mixtures