Extreme Value Theory (EVT) deals with the analysis of rare events and it has been recently used in finance to predict the occurrence of such events, or, at least, to build more robust models for unexpected extreme events. Particularly, EVT has been used to model the loss severities in...

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...

We investigate the added value of combining density forecasts for asset return prediction in a specific region of support. We develop a new technique that takes into account model uncertainty by assigning weights to individual predictive densities using a scoring rule based on the censored...

We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns ranging from 1995-2014...

Motivated by the stylized fact that intraday returns can provide additional information on the tail behaviour of daily returns, we propose a functional autoregressive value-at-risk approach which can directly incorporate such informational advantage into the daily value-at-risk forecast. Our...

The historical simulation is a standard technique in market risk estimation, in which the key choice to be made is whether to use absolute or relative shifts for the observed returns of the risk factors. To avoid this ambiguity, Fries et al. develop an approach called displaced historical...

We investigate the effect of estimation error on backtests of (multi-period) expected shortfall (ES) forecasts. These backtests are based on first order conditions of a recently introduced family of jointly consistent loss functions for Value-at-Risk (VaR) and ES. We provide explicit expressions...

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 compare more than 1000 different volatility models in terms of their fit to the historical ISE-100 Index data and their forecasting performance of the conditional variance in an out-of-sample setting. Exponential GARCH model of Nelson (1991) with “constant mean, t-distribution, one lag...

We introduce a structural quantile vector autoregressive (VAR) model. Unlike standard VAR which models only the average interaction of the endogenous variables, quantile VAR models their interaction at any quantile. We show how to estimate and forecast multivariate quantiles within a recursive...