Journal of Applied Finance & Banking

Market Risk Measures using Finite Gaussian Mixtures

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• Abstract

  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.