We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight...

The experience of past financial market turmoil suggests that in addition to eroding investor wealth, the severe consequences of rare extreme market events can spillover and impair the broader real economies. In this context, this paper is an evaluation of the methodological and empirical...

Pareto processes are suitable to model stationary heavy-tailed data. Here, we consider the auto-regressive Gaver–Lewis Pareto Process and address a study of the tail behavior. We characterize its local and long-range dependence. We will see that consecutive observations are asymptotically tail...

The aim of this paper is to define and investigate outlier-proneness for multivariate distributions. This is done by using a concept of ordering multivariate data based on isobar-surfaces, which yields an utmost analogy of the results to the univariate case.

Over the last three decades, the world economy has been facing stock market crashes, currency crisis, the dot-com and real estate bubble burst, credit crunch and banking panics. As a response, extreme value theory (EVT) provides a set of ready-made approaches to risk management analysis....

Goal: ISO 31000 Risk Management (RM) recently re-defined risk as the effect of uncertainty on an organization's ability to meet the objectives. Earlier, it defined risk as a combination of the probability and scope of the (predicted) consequences. The revised ISO Risk advances beyond a static...

Using a limiting approach to portfolio credit risk, we obtain analyticexpressions for the tail behavior of the distribution of credit losses. We showthat in many cases of practical interest the distribution of these losses haspolynomial ('fat') rather than exponential ('thin') tails. Our...