The theme of this dissertation is to study the estimation of portfolio Value-at-Risk and expected shortfall using the combination of GARCH, extreme value theory, copulas, and doubly noncentral t distribution. It includes three papers.

The traditional VaR valuations assume normality of single asset returns and linear correlation as dependence structure. Both assumptions have been criticized heavily. In paper one, we propose a new method which overcome these limits. The new technique is based on Monte Carlo simulation of asset log-returns assuming they have a multivariate distribution with dependence structure characterized by copulas and marginal distributions with empirical distribution function in the center and extreme value distribution in the tail. Also, in order to apply extreme value theory correctly, we filter the log-return series by using GARCH model. To verify the improvement of this new procedure over traditional VaR estimation model, we apply both methods to a portfolio consisting of daily returns on the S&P 500 index and the Nasdaq index. A backtesting technique is utilized to show how the new method outperforms the traditional VaR model.

In paper two, we discuss the theoretical deficiencies of VaR and show that expected shortfall should be implemented as a complementary measure to manage tail risk efficiently. We apply the GARCH-EVT-Copula method proposed in paper one to estimate portfolio expected shortfall. To verify the improvement of our proposed new method over the traditional methods, such as Historical Simulation and traditional Monte Carlo method, we apply all of them to the same portfolio we used in paper one. We use both hypothesis testing and loss functions to evaluate the backtesting results, and we also compare the estimation error for different models.

Most financial assets are characterized by “fat tail”, mild skewness, and strong volatility clustering. In paper three, we present a new methodology for estimating portfolio Value-at-Risk which account for these features of financial data. Our model associates GARCH models with doubly noncentral t distributed errors. We again apply this method to the portfolio used in previous two papers.