In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student’s-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.

This paper proposes a multivariate copula-based volatility model for estimating Value-at-Risk (VaR) in the banking sector of selected European countries by combining dynamic conditional correlation (DCC) multivariate GARCH (M-GARCH) volatility model and copula functions. Nonnormality in multivariate models is associated with the joint probability of the univariate models' marginal probabilities -the joint probability of large market movements, referred to as tail dependence. In this paper, we use copula functions to model the tail dependence of large market movements and test the validity of our results by performing back-testing techniques. The results show that the copula-based approach provides better estimates than the common methods currently used and captures VaR reasonably well based on the differences in the numbers of exceptions produced during different observation periods at the same confidence level.

In this paper, we present a novel approach for forecasting Value-at-Risk (VaR) by combining a Bayesian GARCH(1,1) model with Student's-t distribution for the underlying volatility models, vine copula functions to model dependence, and peaks-over-threshold (POT) method of extreme value theory (EVT) to model the tail behaviour of asset returns. We further propose a new approach for threshold selection in extreme value analysis, which we call a hybrid method. The empirical results and back-testing analysis show that the model captures VaR quite well through periods of calmness and crisis; therefore, it is suitable for use as a measure of risk. Our results also suggest that with a correct implementation of the VaR model, Basel III is not needed.

PurposeThis paper investigates the dependence structure and market risk of the currency exchange rate portfolio from the Malaysian ringgit perspective.Design/methodology/approachThe marginal return of the five major exchange rates series, i.e. United States dollar (USD), Japanese yen (JPY), Singapore dollar (SGD), Thai baht (THB) and Chinese Yuan Renminbi (CNY) are modelled by the Bayesian generalized autoregressive conditional heteroskedasticity (GARCH) (1,1) model with Student's t innovations. In addition, five different copulas, such as Gumbel, Clayton, Frank, Gaussian and Student's t, are applied for modelling the joint distribution for examining the dependence structure of the five currencies. Moreover, the portfolio risk is measured by Value at Risk (VaR) that considers the extreme events through the extreme value theory (EVT).FindingsThe finding shows that Gumbel and Student's t are the best-fitted Archimedean and elliptical copulas, for the five currencies. The dependence structure is asymmetric and heavy tailed.Research limitations/implicationsThe findings of this paper have important implications for diversification decision and hedging problems for investors who involving in foreign currencies. The authors found that the portfolio is diversified with the consideration of extreme events. Therefore, investors who are holding an individual currency with VaR higher than the portfolio may consider adding other currencies used in this paper for hedging.Originality/valueThis is the first paper estimating VaR of a currency exchange rate portfolio using a combination of Bayesian GARCH model, EVT and copula theory. Moreover, the VaR of the currency exchange rate portfolio can be used as a benchmark of the currency exchange market risk.