This paper characterizes the term structure of risk measures such as Value at Risk (VaR) and expected shortfall under different econometric approaches including multivariate regime switching, GARCH-in-mean models with student-t errors, two-component GARCH models and a non-parametric bootstrap. We show how to derive the risk measures for each of these models and document large variations in term...

This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and ...

We introduce a Lagrange Multiplier (LM) test for the constant-correlation hypothesis in a multivariate GARCH model. The test examines the restrictions imposed on a model which encompasses the constant-correlation multivariate GARCH model. It requires the estimates of the constant-correlation model only and is computationally convenient. We report some Monte Carlo results on the "nite-sample pro...

When forecasts are assessed by a general loss (cost-of-error) function, the optimal point forecast is not, in general, the conditional mean, and depends on the conditional volatility – which, for stock returns, is time-varying. Our aim is to provide forecasts of daily returns of 30 DJIA stocks under a general multivariate loss function. The paper’s contributions are as follows. We discuss what ...

After the so-called Asia crisis in the summer of 1997 the nancial markets were shaken by increased volatility transmission around the world. Therefore, in this paper we will analyse the daily exchange rates in New York, Germany, and Japan for the period of 2 years (June 21, 1996 to June 22, 1998). We estimate a VAR-GARCH in mean model and estimate the multivariate volatility e ects between the ...

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non-parametric approaches for GARCH models that avoid imposing arbitrary pa...

This paper introduces quasi-maximum likelihood estimator for multivariate diffusions based on discrete observations. A numerical solution to the stochastic differential equation is obtained by higher order Wagner-Platen approximation and it is used to derive the first two conditional moments. Monte Carlo simulation shows that the proposed method has good finite sample property for both normal a...