This study proposes a new approach for estimating value at risk (VaR). This approach combines quasi-maximum-likelihood fitting of asymmetric conditional autoregressive range (ACARR) models to estimate the current volatility and classical extreme value theory (EVT) to estimate the tail of the...

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...

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...

Forecasting-volatility models typically rely on either daily or high frequency (HF) data and the choice between these two categories is not obvious. In particular, the latter allows to treat volatility as observable but they suffer of many limitations. HF data feature microstructure problem,...

This article looks at the theory and empirics of extremal quantiles in economics, in particular value-at-risk. The theory of extremes has gone through remarkable developments and produced valuable empirical findings in the last 20 years. In the discussion, we put a particular focus on...