Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected shortfall-or the trading book model...

In this study, we examine different quantitative methods to recover the risk neutral distribution function associated to the prices of option on bank shares. This is useful for a wide range of applications, such as determining the implicit State guarantee that systemic financial institutions...

We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk. The asymptotic limits are...

In this study we consider the risk estimation as a stochastic process based on the Sample Quantile Process (SQP) - which is a generalization of the Value-at-Risk calculated on a rolling sample. Using SQP's, we are able to show and quantify the pro-cyclicality of the current way financial...

We investigate the asymptotics for two geometric measures, geometric quantiles and halfspace depths. While much literature is known on the population side, we fill out some gaps there to obtain a full picture, before turning to the sample versions, where the questions on asymptotics become...