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There are various metrics for financial risk, such as value at risk (VaR),expected shortfall, expected/unexpected loss, etc. When estimating thesemetrics, it was very common to assume Gaussian distribution for the assetreturns, which may underestimate the real risk of the market, especially duringthe financial crisis. In this paper, we propose a series of time-varyingmixture models for risk analysis and management. These mixture models containtwo components: one component with Gaussian distribution, and the other onewith a fat-tailed Cauchy distribution. We allow the distribution parameters andcomponent weights to change over time to increase the flexibility of themodels. Monte Carlo Expectation-Maximization algorithm is utilized to estimatethe parameters. To verify the good performance of our models, we conduct somesimulation studies, and implement our models to the real stock market. Based onthese studies, our models are appropriate under different economic conditions,and the component weights can capture the correct pattern of the marketvolatility.

Time-Varying Gaussian-Cauchy Mixture Models for Financial Risk Management