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

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