Refining Value-at-Risk estimates: An Extreme Value Theory Approach

This thesis proposes new approaches to Value-at-Risk estimation using (1) Multivariate GARCH Dynamic Conditional Correlation volatility model with skewed Student’s-t distributions, (2) Bayesian GARCH model with Student’s-t distribution, and (3) Bayesian Markov-Switching GJR-GARCH model with skewed Student’s-t distributions, incorporating copula functions and extreme value theory. A new approach for selecting a proper threshold in the Peaks Over Threshold method for extreme value theory analysis called the hybrid method is also proposed. The proposed Value-at-Risk models are compared to the traditional Value-at-Risk models commonly used by banks. Back-testing results following Kupiec (1995) unconditional coverage test, Christoffersen (1998) independent and conditional coverage test, Basel traffic light test, Santos and Alves (2012) new independent test, Dowd (2002) bootstrap back-test, and Engle and Manganelli (2004) Dynamic Quantile test show that Value-at-Risk models constructed following extreme value theory produced reliable Value-at-Risk estimates. Furthermore, Value-at-Risk models incorporating the hybrid method for threshold selection produced more stable Value-at-Risk estimates compared to the traditional Value-at-Risk models.