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This study aims to implement a novel approach of using the Realized generalized autoregressive conditional heteroskedasticity (GARCH) model within the conditional extreme value theory (EVT) framework to generate quantile forecasts. The Realized GARCH-EVT models are estimated with different realized volatility measures. The forecasting ability of the Realized GARCH-EVT models is compared with that of the standard GARCH-EVT models.

One-step-ahead forecasts of Value-at-Risk (VaR) and expected shortfall (ES) for five European stock indices, using different two-stage GARCH-EVT models, are generated. The forecasting ability of the standard GARCH-EVT model and the asymmetric exponential GARCH (EGARCH)-EVT model is compared with that of the Realized GARCH-EVT model. Additionally, five realized volatility measures are used to test whether the choice of realized volatility measure affects the forecasting performance of the Realized GARCH-EVT model.

In terms of the out-of-sample comparisons, the Realized GARCH-EVT models generally outperform the standard GARCH-EVT and EGARCH-EVT models. However, the choice of the realized estimator does not affect the forecasting ability of the Realized GARCH-EVT model.

It is one of the earliest implementations of the two-stage Realized GARCH-EVT model for generating quantile forecasts. To the best of the authors’ knowledge, this is the first study that compares the performance of different realized estimators within Realized GARCH-EVT framework. In the context of high-frequency data-based forecasting studies, a sample period of around 11 years is reasonably large. More importantly, the data set has a cross-sectional dimension with multiple European stock indices, whereas most of the earlier studies are based on the US market.

This paper aims to investigate whether the best statistical model also corresponds to the best empirical performance in the volatility modeling of financialized commodity markets.

The authors use various p and q values in Value-at-Risk (VaR) GARCH(p, q) estimation and perform backtesting at different confidence levels, different out-of-sample periods and different data frequencies for eight financialized commodities.

They find that the best fitted GARCH(p,q) model tends to generate the best empirical performance for most financialized commodities. Their findings are consistent at different confidence levels and different out-of-sample periods. However, the strong results occur for both daily and weekly returns series. They obtain weak results for the monthly series.

Their research method is limited to the GARCH(p,q) model and the eight discussed financialized commodities.

They conclude that they should continue to rely on the log-likelihood statistical criteria for choosing a GARCH(p,q) model in financialized commodity markets for daily and weekly forecasting horizons.

The log-likelihood statistical criterion has strong predictive power in GARCH high-frequency data series (daily and weekly). This finding justifies the importance of using statistical criterion in financial market modeling.

First, this paper investigates whether the best statistical model corresponds to the best empirical performance. Second, this paper provides an indirect test for evaluating the accuracy of volatility modeling by using the VaR approach.

The purpose of this paper is to compare the daily conditional variance forecasts of seven GARCH-family models. This paper investigates whether the advanced GARCH models outperform the standard GARCH model in forecasting the variance of stock indices.

Using the daily price observations of 21 stock indices of the world, this paper forecasts one-step-ahead conditional variance with each forecasting model, for the period 1 January 2000 to 30 November 2013. The forecasts are then compared using multiple statistical tests.

It is found that the standard GARCH model outperforms the more advanced GARCH models, and provides the best one-step-ahead forecasts of the daily conditional variance. The results are robust to the choice of performance evaluation criteria, different market conditions and the data-snooping bias.

This study addresses the data-snooping problem by using an extensive cross-sectional data set and the superior predictive ability test (Hansen, 2005). Moreover, it covers a sample period of 13 years, which is relatively long for the volatility forecasting studies. It is one of the earliest attempts to examine the impact of market conditions on the forecasting performance of GARCH models. This study allows for a rich choice of parameterization in the GARCH models, and it uses a wide range of performance evaluation criteria, including statistical loss functions and the Mince-Zarnowitz regressions (Mincer and Zarnowitz 1969). Therefore, the results are more robust and widely applicable as compared to the earlier studies.

The purpose of this paper is to examine the impact of structural breaks on the conditional variance of carbon emission allowance prices.

The authors employ the symmetric GARCH model, and two asymmetric models, namely the exponential GARCH and the threshold GARCH.

The authors show that the forecast performance of GARCH models improves after accounting for potential structural changes. Importantly, we observe a significant drop in the volatility persistence of emission prices. In addition, the effects of positive and negative shocks on carbon market volatility increase when breaks are taken into account. Overall, the findings reveal that when structural breaks are ignored in the emission price risk, the volatility persistence is overestimated and the news impact is underestimated.

The authors are the first to examine how the conditional variance of carbon emission allowance prices reacts to structural breaks.

This present work aims at looking into whether or not introducing commodities in international equity portfolios helps reduce the market risk and if hedging is carried out with the same effectiveness across different regional stock markets.

The authors determine the optimal hedge ratios and hedging effectiveness of a number of commodity-hedged emerging and developed equity markets, using three versions of MGARCH model: DCC, ADCC and GO-GARCH. The authors also use a rolling window estimation procedure for the purpose of constructing out-of-sample one-step-ahead forecasts of dynamic conditional correlations and optimal hedge ratios.

Empirical results evince that commodities significantly display effective risk-reducing hedge instruments in short and long runs. The main finding is that commodities do not seem to hedge regional stock markets in the same way. They tend to provide evidence of a rather effective hedging regarding mainly the East European and Latin American stock markets.

The authors study whether commodities can hedge stock markets at regional context and if hedging effectiveness differ from one region to another.

In Islamic finance (IF), the safety-first rule of investing (hifdh al mal) is held to be of utmost importance. In view of the instability in the global financial markets, the IF portfolio manager (mudharib) is committed, according to Sharia, to make use of advanced models and reliable tools. This paper seeks to address these issues.

In this paper, the limitations of the standard models used in the IF industry are reviewed. Then, a framework was set forth for a reliable modeling of the IF markets, especially in extreme events and highly volatile periods. Based on the empirical evidence, the framework offers an improved tool to ameliorate the evaluation of Islamic stock market risk exposure and to reduce the costs of Islamic risk management.

Based on the empirical evidence, the framework offers an improved tool to ameliorate the evaluation of Islamic stock market risk exposure and to reduce the costs of Islamic risk management.

In IF, the portfolio manager – mudharib – according to Sharia, should ensure the adequacy of the mathematical and statistical tools used to model and control portfolio risk. This task became more complicated because of the increase in risk, as measured via market volatility, during the financial crisis that began in the summer of 2007. Sharia condemns the portfolio manager who demonstrates negligence and may hold him accountable for losses for failing to select the proper analytical tools. As Sharia guidelines hold the safety-first principle of investing rule (hifdh al mal) to be of utmost importance, the portfolio manager should avoid speculative investments and strategies that would lead to significant losses during periods of high market volatility.

The purpose of this paper is to propose two hybrid forecasting models which integrate available ones. A hybrid contaminated normal distribution (CND) model accurately reflects the non‐normal features of monthly S&P 500 index returns, and a hybrid GARCH model captures a serial correlation with respect to volatility. The hybrid GARCH model potentially enables financial institutions to evaluate long‐term investment risks in the S&P 500 index more accurately than current models.

The probability distribution of an expected investment outcome is generated with a Monte Carlo simulation. A taller peak and fatter tails (kurtosis), which the probability distribution of monthly S&P 500 index returns contains, is produced by integrating a CND model and a bootstrapping model. The serial correlation of volatilities is simulated by applying a GARCH model.

The hybrid CND model can simulate the non‐normality of monthly S&P 500 index returns, while avoiding the influence of discrete observations. The hybrid GARCH model, by contrast, can simulate the serial correlation of S&P 500 index volatilities, while generating fatter tails. Long‐term investment risks in the S&P 500 index are affected by the serial correlation of volatilities, not the non‐normality of returns.

The hybrid models are applied only to the S&P 500 index. Cross‐sectional correlations among different asset groups are not examined.

The proposed hybrid models are unique because they combine available ones with a decision tree algorithm. In addition, the paper clearly explains the strengths and weaknesses of existing forecasting models.

Financial returns are often modeled as stationary time series with innovations having heteroscedastic conditional variances. This paper seeks to derive the kurtosis of stationary processes with GARCH errors. The problem of hypothesis testing for stationary ARMA(p, q) processes with GARCH errors is studied. Forecasting of ARMA(p, q) processes with GARCH errors is also discussed in some detail.

Estimating‐function methodology was the principal method used for the research. The results were also illustrated using examples and simulation studies. Volatility modeling is the subject of the paper.

The kurtosis of stationary processes with GARCH errors is derived in terms of the model parameters (ψ), Ψ‐weights, and the kurtosis of the innovation process. Hypothesis testing for stationary ARMA(p, q) processes with GARCH errors based on the estimating‐function approach is shown to be superior to the least‐squares approach. The fourth moment of the l‐steps‐ahead forecast error is related to the model parameters and the kurtosis of the innovation process.

This paper will be of value to econometricians and to anyone with an interest in the statistical properties of volatility modeling.

This paper compares the out-of-sample forecasting performance of three long-memory volatility models (i.e., fractionally integrated (FI), break and regime switching) against three short-memory models (i.e., GARCH, GJR and volatility component). Using S&P 500 returns, we find that structural break models produced the best out-of-sample forecasts, if future volatility breaks are known. Without knowing the future breaks, GJR models produced the best short-horizon forecasts and FI models dominated for volatility forecasts of 10 days and beyond. The results suggest that S&P 500 volatility is non-stationary at least in some time periods. Controlling for extreme events (e.g., the 1987 crash) significantly improved forecasting performance.