| Motivated by understanding the devastating financial crisis in 2008 that was partially caused by underestimation of financial risk, we propose a class of time-varying mixture models for risk analysis and management. There are various metrics for financial risk including value at risk (VaR), expected shortfall, expected / unexpected loss, etc. In this study we focus on VaR and one commonly used method to estimate VaR is the Variance-Covariance method, in which normal distribution is usually assumed for asset returns that may underestimate the real risk. To address this issue, in this study we propose a series of two-component mixture models - one component is normal distribution and the other is a fat-tailed distribution such as Cauchy distribution, student's t-distribution or Gumbel distribution. Instead of assuming distribution parameters and weights to be constant, we allow them to change over time which guarantees exibility of our models. Monte Carlo Expectation-Maximization method and Monte Carlo maximum likelihood estimation were used for parameter estimation. Simulation studies are conducted and the models are applied in stock market price data. |
