Background: In light of the latest global financial crisis and the ongoing sovereign debt crisis, accurate measuring of market losses has become a very current issue. One of the most popular risk measures is Value-at-Risk (VaR). Objectives: Our paper has two main purposes. The first is to test the relative performance of selected GARCH-type models in terms of their ability of delivering volatil...

We examine the impact of adding either a VaR or a CVaR constraint to the mean–variance model when security returns are assumed to have a discrete distribution with finitely many jump points. Three main results are obtained. First, portfolios on the VaR-constrained boundary exhibit (K + 2)-fund separation, where K is the number of states for which the portfolios suffer losses equal to the VaR bo...

This paper studies a facility location model with fuzzy random parameters and its swarm intelligence approach. A Value-at-Risk (VaR) based fuzzy random facility location model (VaR-FRFLM) is built in which both the costs and demands are assumed to be fuzzy random variables, and the capacity of each facility is unfixed but a decision variable assuming continuous values. Under this setting, the V...

This paper measured the value at risk (VaR) and expected shortfall (ES) of the US Treasury yield changes. The US Treasury yield data were tested and found to be not normally distributed. Consequently, the mixture normal model (MNM) was used to improve the delta normal VaR and ES measures. It performed extraordinarily well in all cases, based on bootstrapping and mean square error tests. In addi...

In credit risk modelling, the correlation of unobservable asset returns is a crucial component for the measurement of portfolio risk. In this paper, we estimate asset correlations from monthly time series of Moody’s KMV asset values for around 2,000 European firms from 1996 to 2004. We compare correlation and value-atrisk (VaR) estimates in a one–factor or market model and a multi-factor or sec...

One of the most commonly used methods for modeling multivariate time series is the Vector Autoregressive Model (VAR). VAR is generally used to identify lead, lag and contemporaneous relationships describing Granger causality within and between time series. In this paper, we investigate VAR methodology for analyzing data consisting of multilayer time series which are spatially interdependent. Wh...

In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, i.e., what is the maximum and minimum Value-at-Risk (VaR) that can be justified given a certain amount of available information. Puccetti and Rüschendorf (2012b) and Embrechts et al. (2013) propose the rearrangement algorithm (RA) as a general method to approximate VaR bounds when the default probabilit...

In this paper the value at risk (VaR) forecasts are compared using three different GARCH models; ARCH(1), GARCH(1,1) and EGARCH(1,1). The implemented method is a one-day ahead out of sample forecast of the VaR. The forecasts are evaluated using the Kupiec test with a five percent significance level. The focus is on three different markets; commodities, equities and exchange rates. The goal of t...

Research related to aggregation, robustness, and model uncertainty of regulatory risk measures, for instance, Value-at-Risk (VaR) and Expected Shortfall (ES), is of fundamental importance within quantitative risk management. In risk aggregation, marginal risks and their dependence structure are often modeled separately, leading to uncertainty arising at the level of a joint model. In this paper...