Extremal financial risk models and portfolio evaluation

It is difficult to find an existing single model which is able to simultaneously model exceedances over thresholds in multivariate financial time series. A new modeling approach, which is a combination of max-stable processes, GARCH processes, and Markov processes, is proposed. Combining Markov processes and max-stable processes defines a new statistical model which has the flexibility of modeling cross-sectional tail dependencies between risk factors and tail dependencies across time. The new model also models asymmetric behaviors of negative and positive returns on financial assets. An important application of the proposed method is to calculate VaRs (Value at Risk) and evaluate portfolio combinations under VaR constraints. Result comparisons between VaRs based on the new approach and VaRs based on some existing methods such as variance-covariance approach and historical simulation approach suggest that some existing methods substantially underestimate the risks during recession and expansion time.