Dependency Modeling and Value-at-Risk Forecasts for Financial Portfolios
Forecasting Value-at-Risk (VaR) for financial portfolios is a staggering task in financial risk management. The turmoil in financial markets as observed since September 2008 called for more complex VaR models, as "standard" VaR approaches failed to anticipate the collective market movements faced during the financial crisis. Hence, recent researchon portfolio management mainly focused on modeling return interdependencies via dynamic conditional correlations (DCC, Engle (2002)) volatility spillover (e.g. the BEKK model, named after Baba, Engle, Kraft and Kroner, (1995)) or copulas (Embrechts et al. (2002)).
In this contribution, VaR estimates based on extreme value theory (EVT) models combined with elliptical copulas are analyzed. Tails of the return distributions are modeled via Generalized Pareto Distribution (GPD) approaches applied to GARCH filtered residuals to capture excess returns. Copula models are used to account for tail dependence. Drawing on this EVT-GARCH-Copula approach, portfolios consisting of German Stocks, national indices and FX-rates, with a data sample covering both calm and turmoil market phases are evaluated.
Moreover, models accounting for variable and invariant dependency schemes are evaluated using statistical backtesting and Basel II criteria.