This appendix extends simulation and empirical results reported in Mancini and Trojani (2010). It discusses the choice of the robustness tuning constants; describes the unconditional, independence and conditional coverage tests for VaR forecast evaluation; provides additional Monte Carlo...

We analyze the impact of the estimation frequency - updating parameter estimates on a daily, weekly, monthly or quarterly basis - for commonly used GARCH models in a large-scale study, using more than twelve years (2000-2012) of daily returns for constituents of the S&P 500 index. We assess the...

We describe characteristics of various risk measures (Value-at-Risk, Expected Shortfall, etc.) that are used to analyze and quantify the tail risk exposure, and discuss their relative strengths and weaknesses. Emphasis is placed on presenting and comparing methodologies to compute and backtest...

We investigate capital requirements based on Value at Risk (V@R) and Average Value at Risk (AV@R) when the bank's econometric model only approximately describes the true, unknown return generating process, as is often the case in practice. We provide a simple formula for such capital...

This paper poses a new methodology to estimate the required economic capital for a retail-credit portfolio. The methodology is based on both the general copula concepts and some core results from the extreme value theory (EVT). The main results support the fact that the proposed methodology is...

In a banking network model, the ranking consistency of various popular systemic risk measures (SRMs) is analyzed. In contrast to previous studies, this model-based analysis offers the advantage that the sensitivity of the ranking consistency with respect to bank and network characteristics can...

We study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modeled probability level. The choice of the kernel function makes explicit the user's priorities for model performance. The class...

Our data, relating to a period of extreme market turmoil, show typical leptokurtosis and skewness, leading us to consider the skewed exponential power distribution of Fernández et al. (1995), referred to as the SEP3. We demonstrate that the conditional forecasting of VaR and CVaR, made up of a...

We demonstrate how a mixture of two SEP3 densities (skewed exponential power distribution of Fernández et al., 1995) can model the conditional forecasting of VaR and CVaR to efficiently cover market risk at regulatory levels of 1% and 2.5%, as well as at the additional 5% level. Our data...