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This study aims to use a novel methodology to investigate the performance of several multivariate value at risk (VaR) and expected shortfall (ES) models implemented to assess the risk of an equally weighted portfolio consisting of high-frequency (1-min) observations for five foreign currencies, namely, EUR/USD, GBP/USD, EUR/JPY, USD/JPY and GBP/JPY.

By applying the multiplicative component generalised autoregressive conditional heteroskedasticity (MC-GARCH) model on each return series and by modelling the dependence structure using copulas, the 95 per cent intraday portfolio VaR and ES are forecasted for an out-of-sample set using Monte Carlo simulation.

In terms of VaR forecasting performance, the backtesting results indicated that four out of the five models implemented could not be rejected at 5 per cent level of significance. However, when the models were further evaluated for their ES forecasting power, only the Student’s t and Clayton models could not be rejected. The fact that some ES models were rejected at 5 per cent significance level highlights the importance of selecting an appropriate copula model for the dependence structure.

To the best of the authors’ knowledge, this is the first study to use the MC-GARCH and copula models to forecast, for the next 1 min, the VaR and ES of an equally weighted portfolio of foreign currencies. It is also the first study to analyse the performance of the MC-GARCH model under seven distributional assumptions for the innovation term.

The purpose of the paper is to better measure the risks and volatility of the Bitcoin market by using the proposed novel risk measurement model.

The joint regression analysis of value at risk (VaR) and expected shortfall (ES) can effectively overcome the non-elicitability problem of ES to better measure the risks and volatility of financial markets. And because of the incomparable advantages of the long- and short-term memory (LSTM) model in processing non-linear time series, the paper embeds LSTM into the joint regression combined forecasting framework of VaR and ES, constructs a joint regression combined forecasting model based on LSTM for jointly measuring VaR and ES, i.e. the LSTM-joint-combined (LSTM-J-C) model, and uses it to investigate the risks of the Bitcoin market.

Empirical results show that the proposed LSTM-J-C model can improve forecasting performance of VaR and ES in the Bitcoin market more effectively compared with the historical simulation, the GARCH model and the joint regression combined forecasting model.

The proposed LSTM-J-C model can provide theoretical support and practical guidance to cryptocurrency market investors, policy makers and regulatory agencies for measuring and controlling cryptocurrency market risks.

A novel risk measurement model, namely LSTM-J-C model, is proposed to jointly estimate VaR and ES of Bitcoin. On the other hand, the proposed LSTM-J-C model provides risk managers more accurate forecasts of volatility in the Bitcoin market.

The existing literature on the Black-Litterman (BL) model does not offer adequate guidance on how to generate investors’ views in an objective manner. Therefore, the purpose of this paper is to establish a generalized multivariate Vector Error Correction Model (VECM)/Vector Auto-Regressive (VAR)-Dynamic Conditional Correlation (DCC)/Asymmetric DCC (ADCC) framework, and applies it to generate objective views to improve the practicality of the BL model.

This paper establishes a generalized VECM/VAR-DCC/ADCC framework that can be utilized to model multivariate financial time series in general, and produce objective views as inputs to the BL model in particular. To test the VECM/VAR-DCC/ADCC preconditioned BL model’s practical utility, it is applied to a six-asset China portfolio (including one risk-free asset).

With dynamically optimized view confidence parameters, the VECM/VAR-DCC/ADCC preconditioned BL model offers clear advantage over the standard mean-variance method, and provides an automated portfolio optimization alternative to the classic BL approach.

The VECM/VAR-DCC/ADCC framework and its application in the BL model proposed by this paper provide an alternative approach to the classic BL method. Since all the view parameters, including estimated mean return vectors, conditional covariance matrices and pick matrices, are generated in the VECM/VAR and DCC/ADCC preconditioning stage, the model improves the objectiveness of the inputs to the BL stage. In conclusion, the proposed model offers a practical choice for automated portfolio balancing and optimization in a China context.

The purpose of this paper is to compare the performance of commonly used value at risk (VaR) estimation methods for equity indices from both developed countries and emerging markets.

In addition to traditional time‐series models, this paper examines the recently developed nonparametric kernel estimator (KE) approach to predicting VaR. KE methods model tail behaviors directly and independently of the overall return distribution, so are better able to take into account recent extreme shocks.

The paper compares the performance and reliability of five major VaR methodologies, using more than 26 years of return data on 37 equity indices. Through back‐testing of the resulting models on a moving window and likelihood ratio tests, it shows that KE models produce remarkably good VaR estimates and outperform the other common methods.

Financial assets are known to have irregular return patterns; not only the volatility but also the distributions themselves vary over time. This analysis demonstrates that a nonparametric approach (the KE method) can generate reliable VaR estimates and accurately capture the downside risk.

The paper evaluates the performance of several common VaR estimation approaches using a comprehensive sample of empirical data. The paper also reveals that kernel estimation methods can achieve remarkably reliable VaR forecasts. A detailed and complete investigation of nonparametric estimation methods will therefore significantly contribute to the understanding of the VaR estimation processes.

The purpose of the paper is to back-test value-at-risk (VaR) models for conditional distributions belonging to a Generalized Hyperbolic (GH) family of Lévy processes – Variance Gamma, Normal Inverse Gaussian, Hyperbolic distribution and GH – and compare their risk-management features with a traditional unconditional extreme value (EV) approach using data from future contracts return data of S&P500, FTSE100, DAX, HangSeng and Nikkei 225 indices.

The authors apply tail-based and Lévy-based calibration to estimate the parameters of the models as part of the initial data analysis. While the authors utilize the peaks-over-threshold approach for generalized Pareto distribution, the conditional maximum likelihood method is followed in case of Lévy models. As the Lévy models do not have closed form expressions for VaR, the authors follow a bootstrap method to determine the VaR and the confidence intervals. Finally, for back-testing, they use both static calibration (on the entire data) and dynamic calibration (on a four-year rolling window) to test the unconditional, independence and conditional coverage hypotheses implemented with 95 and 99 per cent VaRs.

Both EV and Lévy models provide the authors with a conservative proportion of violation for VaR forecasts. A model targeting tail or fitting the entire distribution has little effect on either VaR calculation or a VaR model’s back-testing performance.

To the best of the authors’ knowledge, this is the first study to explore the back-testing performance of Lévy-based VaR models. The authors conduct various calibration and bootstrap techniques to test the unconditional, independence and conditional coverage hypotheses for the VaRs.

The purpose of this paper is to focus on the performance of three alternative value‐at‐risk (VaR) models to provide suitable estimates for measuring and forecasting market risk. The data sample consists of five international developed and emerging stock market indices over the time period from 2004 to 2008. The main research question is related to the performance of widely‐accepted and simplified approaches to estimate VaR before and after the financial crisis.

VaR is estimated using daily data from the UK (FTSE 100), Germany (DAX30), the USA (S&P500), Turkey (ISE National 100) and Greece (GRAGENL). Methods adopted to calculate VaR are: EWMA of Riskmetrics; classic GARCH(1,1) model of conditional variance assuming a conditional normally distributed returns; and asymmetric GARCH with skewed Student‐t distributed standardized innovations.

The paper provides evidence that the tools of quantitative finance may achieve their objective. The results indicate that the widely accepted and simplified ARCH framework seems to provide satisfactory forecasts of VaR, not only for the pre‐2008 period of the financial crisis but also for the period of high volatility of stock market returns. Thus, the blame for financial crisis should not be cast upon quantitative techniques, used to measure and forecast market risk, alone.

Knowledge of modern risk management techniques is required to resolve the next financial crisis. The next crisis can be avoided only when financial risk managers acquire the necessary quantitative skills to measure uncertainty and understand risk.

The main contribution of this paper is that it provides evidence that widely accepted/used methods give reliable VaR estimates and forecasts for periods of financial turbulence (financial crises).

The purpose of this paper is to apply alternative GARCH‐type models to daily volatility forecasting, and apply Value‐at‐Risk (VaR) to the Taiwanese stock index futures markets that suffered most from the global financial tsunami that occurred during 2008.

Rather than using squared returns as a proxy for true volatility, this study adopts three range‐based proxies (PK, GK and RS), and one return‐based proxy (realized volatility), for use in the empirical exercise. The forecast evaluation is conducted using various proxy measures based on both symmetric and asymmetric loss functions, while back‐testing and two utility‐based loss functions are employed for further VaR assessment with respect to risk management practice.

Empirical results demonstrate that the EGARCH model provides the most accurate daily volatility forecasts, while the performances of the standard GARCH model and the GARCH models with highly persistent and long‐memory characteristics are relatively poor. In the area of risk management, the RV‐VaR model tends to underestimate VaR and has been rejected owing to a lack of correct unconditional coverage. In contrast, the GARCH genre of models can provide satisfactory and reliable daily VaR forecasts.

The unobservable volatility can be proxied using parsimonious daily price range with freely available prices when applied to Taiwanese futures markets. Meanwhile, the GARCH‐type models remain valid downside risk measures for both regulators and firms in the face of a turbulent market.

This paper aims to indirectly evaluate the accuracy of various volatility models using a value-at-risk (VaR) approach and to investigate the relationship between the accuracy of volatility modelling and investments performance in the financialized commodity markets.

This paper uses the VaR back-testing approach at six different commodities, seven different volatility models and five different time horizons.

This paper finds that the moving average (MA) VaR model tends to be the best for oil, copper, wheat and corn (long horizon) whereas the exponential generalized autoregressive conditional heteroscedastic (E-GARCH) VaR model tends to be the best for gold, silver and corn (short horizon). Our findings indicate that MA volatility model should be used for oil, copper, wheat and corn (for longer time horizons) commodities whereas E-GARCH volatility model should be used for gold, silver and corn (for short time horizons) commodities. We also find that there is a positive relationship between an accurate VaR performance and commodity return. This indicates that a good job in modelling volatility will be rewarded by higher returns in financialized commodity markets.

This paper indirectly evaluates the accuracy of volatility model via VaR measure and investigates the relationship between the accuracy of volatility and investments performance in financialized commodity markets. This paper contributes to the literature by offering VaR approach in evaluating volatility model performance and reporting the importance of performing accurate volatility modelling in financialized commodity markets.

Aims to investigate the accuracy of parametric, nonparametric, and semiparametric methods in predicting the one‐day‐ahead value‐at‐risk (VaR) measure in three types of markets (stock exchanges, commodities, and exchange rates), both for long and short trading positions.

The risk management techniques are designed to capture the main characteristics of asset returns, such as leptokurtosis and asymmetric distribution, volatility clustering, asymmetric relationship between stock returns and conditional variance, and power transformation of conditional variance.

Based on back‐testing measures and a loss function evaluation method, finds that the modeling of the main characteristics of asset returns produces the most accurate VaR forecasts. Especially for the high confidence levels, a risk manager must employ different volatility techniques in order to forecast accurately the VaR for the two trading positions.

Different models achieve accurate VaR forecasts for long and short trading positions, indicating to portfolio managers the significance of modeling separately the left and the right side of the distribution of returns.

The behavior of the risk management techniques is examined for both long and short VaR trading positions; to the best of one's knowledge, this is the first study that investigates the risk characteristics of three different financial markets simultaneously. Moreover, a two‐stage model selection is implemented in contrast with the most commonly used back‐testing procedures to identify a unique model. Finally, parametric, nonparametric, and semiparametric techniques are employed to investigate their performance in a unified environment.

This study aims to forecast daily value-at-risk (VaR) for international stock indices by using the conditional extreme value theory (EVT) with the Realized GARCH (RGARCH) model. The predictive ability of this Realized GARCH-EVT (RG-EVT) model is compared with those of the standalone GARCH models and the conditional EVT specifications with standard GARCH models.

The authors use daily data on returns and realized volatilities for 13 international stock indices for the period from 1 January 2003 to 8 October 2014. One-step-ahead VaR forecasts are generated using six forecasting models: GARCH, EGARCH, RGARCH, GARCH-EVT, EGARCH-EVT and RG-EVT. The EVT models are implemented using the two-stage conditional EVT framework of McNeil and Frey (2000). The forecasting performance is evaluated using multiple statistical tests to ensure the robustness of the results.

The authors find that regardless of the choice of the GARCH model, the two-stage conditional EVT approach provides significantly better out-of-sample performance than the standalone GARCH model. The standalone RGARCH model does not perform better than the GARCH and EGARCH models. However, using the RGARCH model in the first stage of the conditional EVT approach leads to a significant improvement in the VaR forecasting performance. Overall, among the six forecasting models, the RG-EVT model provides the best forecasts of daily VaR.

To the best of the authors’ knowledge, this is the earliest implementation of the RGARCH model within the conditional EVT framework. Additionally, the authors use a data set with a reasonably long sample period (around 11 years) in the context of high-frequency data-based forecasting studies. More significantly, the data set has a cross-sectional dimension that is rarely considered in the existing VaR forecasting literature. Therefore, the findings are likely to be widely applicable and are robust to the data snooping bias.