Backtesting risk measures represents a challenge and complex methods are often required. In this paper, we propose a new framework for backtesting that can be applied to every law invariant risk measures. We base our approach on the formalization of the concept of level of coverage associated...

The aim of the presented study was to assess the quality of VaR forecasts in various states of the economic situation. Two approaches based on the extreme value theory were compared: Block Maxima and the Peaks Over Threshold. Forecasts were made on the daily closing prices of 10 major indices in...

This paper demonstrates that existing quantile regression models used for forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. A Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as...

In this study, we investigate the cross-section of option implied tail risks in commodity markets. In contrast to findings from equity markets, left and right tail risk implied by option markets are both large. Commodity specific variables exert the largest influence on tail risk, while there is...

We comprehensively investigate the usefulness of tail risk measures proposed in the literature. We evaluate both the statistical and the economic validity of the measures. The option-implied measure of Bollerslev and Todorov (2011b) (BT11Q) performs the best overall. While some other tail risk...

This paper revisits the performance of frequently used risk forecasting methods, such as the Value-at-Risk models. The aim is to analyze its performance, and mitigate its pitfalls by incorporating conditional variance estimates, as generated by a GARCH model. Notably, this paper tests several...

Linear GARCH(1,1) and GJR GARCH(1,1) processes are established as regularly varying, meaning their heavy tails follow a Power Law, under conditions that allow the innovations from the, respective, processes to be either symmetrically distributed or skewed. Skewness is considered a stylized fact...

Recently there has been renewed debate about the relative merits of VaR and CVaR as measures of financial risk. VaR is not coherent and does not quantify the risk beyond VaR, while CVaR shows some computational instabilities and is not 'elicitable' (Gneiting 2010, Ziegel 2013). It is argued in...

Financial risk managers routinely use non-linear time series models to predict the downside risk of the capital under management. They also need to evaluate the adequacy of their model using so-called backtesting procedures. The latter involve hypothesis testing and evaluation of loss functions....

The paper deals with maritime risk, which we consider important, no doubt, for ship-owners acting in volatile markets. Traditionally, risk is measured by "standard deviation". Other risk measures like "excess kurtosis", "excess skewness", "long-term dependence" and the "catastrophe propensity"...