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The study examines the relationship and linkages between spot and future prices of European Union Emission Trading Systems (EU-ETS) during 2019–2021. Dynamic conditional correlation specification of multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model was employed to examine the time-varying correlation between spot and future prices. Also, vector autoregression mean model and MGARCH-Baba-Engle-Kroner-Kraft volatility model was jointly estimated to model the spillover between EU ETS spot and future prices in the first and second moments. Lastly, we utilize the variance-covariance matrix of joint mean-variance model estimation to derive the optimal conditional hedge ratio as well as the hedge effectiveness of EU ETS future contracts. Our findings reveal a high conditional correlation and significant spillover between carbon spot and future markets in EU. Further, our study uncovers a high degree of hedge effectiveness for EU ETS future contracts. This is possibly the first study that examines the linkages between EU ETS spot and future prices pertaining to the recent transition stage of phase III and the initial stage of ongoing phase IV of the ETS market. Our findings pinpoint to ETS markets becoming more complete and in turn offering optimal hedging avenues. JEL Codes: G15, C58, Q38 [ABSTRACT FROM AUTHOR]

The volatile nature of the relationship between the stock index and the stocks which stand for it, is revealed. The directions of volatility spillovers are studied in the context of the transformation of causal relationships. The article analyses the interrelationships and volatility spillovers between the S&P-500 index and the shares of META and GOOG (technology sector), JPM and BAC (financial sector), MRO and OXY (oil and gas sector), which are included in the index. The research methodology is based on the GARCH (1,1) model, which allows considering the development of variance over time and the dynamics of conditional volatility of time series. The identified interdependencies are focused on forecasting volatility spillover shocks from the S&P 500 to stocks and vice versa. [ABSTRACT FROM AUTHOR]

The objective of this paper is to provide a deeper insight into the impact of weekly inventory announcements and especially their associated surprises on crude oil returns and volatility during the period from 27 March 2012 to 2 October 2018. The results can be summarized as follows. First, we find that all inventory surprises exert an inverse impact on the oil price returns. Such impact appears more pronounced during the collapse and post‐collapse periods, than during the pre‐collapse period. Second, we show that the reducing volatility effects of inventory shocks that we establish for the whole period are entirely attributed to those observed in the pre‐collapse period. Third, the different effects obtained for positive and negative shocks support evidence that our split of inventory news by nature matters. Fourth, compared to macroeconomic and unconventional monetary news, the inventory statements appear as the most pertinent news during the event window. Fifth, we find evidence also that the effect of the uncertainty about economic stance, when it is significant, changes the way the oil prices and volatility react to inventory surprises, and hence weakens the effectiveness of the inventory policy. Lastly, we make an original use of the information content of the implied volatility to assess the persistence of the link between the conditional variance and the inventory news. The central finding is that the implied volatility enters with a significant effect on the conditional variance for WTI oil returns and namely with a reduced volatility persistence. Also, a significant effect from inventory surprises namely when we split the announcements into negative and positive news is detected even the implied volatility is introduced exogenously in the GARCH‐type variance specification highlighting the predominance of our main variable. [ABSTRACT FROM AUTHOR]

The objective of the research paper is to identify the stock market volatility pattern of brics countries during the outbreak of the covid-19 pandemic. The study is based on the time series data, which consists of the daily closing price of the brics countries' index for a two-year (pandemic) period from1st January 2020 to 31st December 2021. Both the symmetric and asymmetricmodels of Generalized Autoregressive Conditional Heteroscedasticity (garch) have been employed in the study to investigate whether volatility changes over the pandemic period. The result of the garch-m (1, 1) model evidenced the presence of a positive and insignificant risk premium. Based on the empirical work carried out using the market index of brics countries, it was found from egarch (1,1), and tgarch (1,1) models that there exists a leverage effect in the countries, viz. Brazil, Russia, India, China and South Africa. Since the stock price during the pandemic period triggered the entire financial market, the investors, fund managers and portfolio managers should be more aware of the uncertainty and need to adjust their investments accordingly. [ABSTRACT FROM AUTHOR]

This paper investigates the asymmetric behavior of oil price volatility using different types of Asymmetric Power ARCH (APARCH) model. We compare the estimation and forecasting performance of the models estimated from the maximum likelihood estimation (MLE) method and support vector machine (SVM) based regressions. Combining nonparametric SVM method with parametric APARCH model not only enables to keep interpretations of the parametric models but also leads to more precise estimation and forecasting results. Daily or weekly oil price volatility is investigated from March 8, 1991 to September 13, 2019. This whole sample period is split into four sub-periods based on the occurrence of certain economic events, and we examine whether the asymmetric behavior of the volatility exists in each sub-period. Our results indicate that SVM regression generally outperforms the other method with lower estimation and forecasting errors, and it is more robust to the choice of different APARCH models than the MLE counterparts are. Besides, the estimation results of the SVM based regressions in each sub-period show that the ARCH models with asymmetric power generally perform better than the models with symmetric power when the data sub-period includes large swings in oil price. The asymmetric behavior of oil price volatility, however, is not detected when the analysis is done using the whole sample period. This result underscores the importance of identifying the dynamics of the dataset in different periods to improve estimation and forecasting performance in modelling oil price volatility. This paper, therefore, examines volatility behavior of oil price with both methodological and economic underpinnings. [ABSTRACT FROM AUTHOR]

The objective of the research paper is to identify the stock market volatility pattern of BRICS countries during the outbreak of the COVID-19 pandemic. The study is based on the time series data, which consists of the daily closing price of the BRICS countries' index for a two-year (pandemic) period from 1st January 2020 to 31st December 2021. Both the symmetric and asymmetric models of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) have been employed in the study to investigate whether volatility changes over the pandemic period. The result of the GARCH-M (1,1) model evidenced the presence of a positive and insignificant risk premium. Based on the empirical work carried out using the market index of BRICS countries, it was found from EGARCH (1,1), and TGARCH (1,1) models that there exists a leverage effect in the countries, viz. Brazil, Russia, India, China and South Africa. Since the stock price during the pandemic period triggered the entire financial market, the investors, fund managers and portfolio managers should be more aware of the uncertainty and need to adjust their investments accordingly.

This paper presents two different approaches of volatility forecasting. One is based on option‐implied volatility (IV), the other involves conducting time series methods using historical volatility. With that purpose, we study eight developed stock markets, offering implied volatility indexes for the 2008 financial crisis. We evaluated the 1 month out‐of‐sample volatility forecast performance of two statistical‐based models, Mixed Data Sampling (MIDAS) and GARCH, and compared the results with option‐implied volatility indexes. Our results suggest that MIDAS produce superior forecast performance compared to GARCH model and IV method. While options are not available for all assets, we believe that MIDAS model can be a sophisticated tool for researchers and analysts to forecast future volatility with its ability to process high‐frequency data. [ABSTRACT FROM AUTHOR]

Green bonds have gained a significant share in the bond market. However, dynamic risk and its spillover to other conventional bond investments plays an important role in its understanding. In this paper, we analyze the volatility and correlation dynamics between conventional bond and green bond assets under both loose and stringent eligibility green-labeled criteria. We build dynamic conditional correlation (DCC) model specifications using alternative distributional assumptions. We also assess risk dynamics expressed by Value-at-Risk (VaR) and its corresponding loss function. We illustrate risk assessment in within and out-of-sample periods using conventional and green bond returns. The results show that there is significant spillover between conventional and green bond assets, triggering significant hedging strategies. However, these spillover effects are subjected to the type of green-labeled criteria. Finally, a risk assessment using VaR forecasting and its corresponding loss function estimation also demonstrates significant differentiation between green and conventional bonds.

We estimated the stock market risk premium during the COVID-19 pandemic with a GARCH-in-Mean (GARCH-M)(1,1) model. The analysis then explored the presence of regime changes using a two-regime Markov-Switching GARCH (MS GARCH)(1,1) model. The sample we used included the stock market indexes of nine countries from three geographical regions, including: North America (Canada, USA, and Mexico), South America (Brazil and Argentina), and Asia (Japan, South Korea, Hong Kong, and Singapore), over two periods: (a) pre-COVID (from 1 January 2015 to 31 December 2019); and (b) COVID (from 1 January 2020 to 31 December 2021). Our GARCH-M(1,1) estimation results indicate that the more developed countries' stock markets experienced an important increase in their risk premium during the COVID period, likely explained by the massive government anticyclical policies. By contrast, developing countries' stock markets, particularly in Latin America, experienced a reduction, and in some cases, even a total loss of the risk premium effect. From the perspective of investors and portfolio risk managers, the identification of high and low volatility periods and their estimated probability of occurrence is useful for the characterization of stress scenarios and the design of emerging strategies. For governments and central bankers, the implementation of different policies should respond to the more likely scenarios but should also be prepared to respond to other less likely scenarios. Institutional preparedness to respond to as many different scenarios as may be identified with the use of MS GARCH models can make their interventions more successful. This work presents an objective example of how the use of MS GARCH models may be of use to practitioners in both the financial industry and government. We confirmed that the results of a two-regime MS GARCH model are superior to those obtained from a single-regime model. [ABSTRACT FROM AUTHOR]

In this article, novel joint semiparametric spline-based modeling of conditional mean and volatility of financial time series is proposed and evaluated on daily stock return data. The modeling includes functions of lagged response variables and time as predictors. The latter can be viewed as a proxy for omitted economic variables contributing to the underlying dynamics. The conditional mean model is additive. The conditional volatility model is multiplicative and linearized with a logarithmic transformation. In addition, a cube-root power transformation is employed to symmetrize the lagged response variables. Using cubic splines, the model can be written as a multiple linear regression, thereby allowing predictions to be obtained in a simple manner. As outliers are often present in financial data, reliable estimation of the model parameters is achieved by trimmed least-square (TLS) estimation for which a reasonable amount of trimming is suggested. To obtain a parsimonious specification of the model, a new model selection criterion corresponding to TLS is derived. Moreover, the (three-parameter) generalized gamma distribution is identified as suitable for the absolute multiplicative errors and shown to work well for predictions and also for the calculation of quantiles, which is important to determine the value at risk. All model choices are motivated by a detailed analysis of IBM, HP, and SAP daily returns. The prediction performance is compared to the classical generalized autoregressive conditional heteroskedasticity (GARCH) and asymmetric power GARCH (APGARCH) models as well as to a nonstationary time-trend volatility model. The results suggest that the proposed model may possess a high predictive power for future conditional volatility. Supplementary materials for this article are available online.

This article aims to study the impact of peg structure on volatility behaviour and crisis vulnerability, considering the COVID-19 economic context. We adopt a comparative analysis of volatility behaviour using GARCH family models and the ICSS Algorithm for the cases of Morocco and Tunisia. Our main finding is that peg characteristics aren't the unique parameters impacting volatility behaviour and the exposition to the crisis. Furthermore, we detect different variations in volatility parameters as a result of the contrasting economic contexts and COVID-19 economic fallouts. Finally, we present some interesting policy implications, and we suggest some leads for future research. [ABSTRACT FROM AUTHOR]

High diamond price volatility can have significant impact on Botswana's diamond‐driven economy. The global economic crisis of 2008–2009 saw the local economy characterised by heightened commodity price uncertainty, falling stock prices and dwindling international demand for diamonds. In this paper we employ a number of techniques to analyse and assess the effect of diamond price volatility on stock returns in Botswana. Firstly, estimation of a Markov Switching model reveals that high volatility regimes in diamond prices have become more frequent and persistent since the recession. Secondly, a bivariate GARCH‐in‐Mean VAR model is estimated and the results recognize that diamond price volatility has a positive and significant influence on stock returns in Botswana. [ABSTRACT FROM AUTHOR]

Seasonal anomalies cause market inefficiency by affecting the mean and volatility of stock returns, and allow investors to obtain abnormal returns. In Indonesia, there is the month of Sela which is believed as an unlucky month so that many people avoid this month to hold ceremonial activities. As a result, the economy declines in the month of Sela and possibly, the return will also drop in this month. Therefore, this research aims to reveal whether the month of Sela is a seasonal anomaly. This research tested two hypotheses; the effect of the mean and volatility of price index return by using the GARCH model. To examine the effect of the month of Sela on the mean and volatility of return of price index, we collected the data on Indonesian Composite Index and 10 sectoral indices from 2009 to 2019 on three Javanese months, Sawal, Selo and Besar. In total, we collected 7.095 returns data. The month of Sela was a seasonal anomaly that the average and volatility of returns during the month of Sela were lower than those during the months of Sawal and Besar. These results also indicated that during the months of Sawal and Besar, the price index was more volatile than it was during the month of Sela. This research is useful for investors in considering their investment decisions to obtain an abnormal return. This research also contributes to the literature by adding new knowledge about seasonal anomalies that exist in Indonesia.

This article aims to exhibit and study the impacts that changing characteristics of a fixed exchange rate regime has on conditional volatility. To do so, using the U.S. dollar dirham (USDMAD) daily closing rates over 23 years, we compare the GARCH model results of four segmented sub-periods to each other and then to the global period of the study to detect disparities. The main result is that changes in exchange rate regime characteristics do impact the conditional volatility. Therefore, we recommend that the study of conditional volatility should use periods with no changes in the characteristics of the exchange rate regime to avoid bias. Otherwise, the use of segmented sub-periods should be adopted to take account of these changes. Finally, we present some key results about the impacts of these changes in Morocco’s exchange rate regime on the conditional volatility.

The underlying volatility at a given time is called conditional volatility at this particular time and is modeled by various ARMA-GARCH conditional variance equations (GARCH, EGARCH, GJR, APARCH, IGARCH). How important are oil price fluctuations and oil price volatility in foreign exchange markets and stock markets? What is the nature of the relationship between these three markets? What are the political implications if volatility, using appropriate models to determine, turns out to be important? We evaluate these questions empirically, using the specification of Narayan and Narayan (2010). This specification, in our paper, deals with the determination of volatility appropriate models, based on information criteria, of the ARMA-ARCH family conditional volatility of oil returns using daily data for each country independently (i), and revolve around an analysis of the effect of the volatility of black gold price on the returns of the other two markets in Oil Importing Developed Countries category (ii). The selection of appropriate models of oil returns according to the period of the chosen data gives the ARMA(2,2)- GJR(1,2) model for the Germany and the ARMA(2,2)-GJR(2,2) model for the Japan and the USA. The results that the conditional variances of oil returns, foreign exchange market returns and stock market returns are contested and they have a long-term relationship in different countries. In addition, the results of the granger causality tests and the study of impulse response functions have shown that it has a sending effect of the volatility of oil prices on most foreign exchange markets and stock markets, highlighting the strong explanatory power of market volatility, but bidirectional causality is not always present. Our empirical results involved in the prevention of shocks are important for policymakers, for portfolio managers seeking optimal portfolio allocation, for monetary authorities who are studying changes in the exchange rate of the national currency against currencies, for oil-importing countries seeking to minimize their spending on crude oil, and for oil-exporting countries seeking the sound management of oil reserves. They also show that the volatility of crude oil prices on the world market is generally more significant for foreign exchange and stock markets than the volatility of oil price in the local market. This main conclusion gives political implications to policymakers.

This study revisits the topic of predicting aggregate equity returns out-of-sample by conditioning on economic variables through Bayesian model averaging (BMA). Besides simultaneously addressing parameter instability and model uncertainty, I suggest a new model feature, namely, predictors in a given model can also impact the dependent variable through the conditional volatility process. The suggested econometric framework is straightforward to implement without requiring simulation. Likewise, the user can easily decide, which aspects of the predictive channel should to be switched on, off or altered. I apply the suggested framework to the well-known [Goyal, A. and Welch, I., A comprehensive look at the empirical performance of equity premium prediction. Rev. Financial Stud., 2008, 21, 1455–1508] dataset. An extensive out-of-sample prediction evaluation demonstrates that averaging over predictor combinations in a model that allows lagged predictors to impact aggregate equity returns exclusively through the conditional volatility process results in statistically significant more accurate density predictions relative to the benchmark, especially when predicting the left tail of the conditional distribution. One also observes economic gains in favor of certain BMAs. Here, the BMA that allows predictors to impact equity returns through the conditional mean as well as the conditional volatility process is the top performer. [ABSTRACT FROM AUTHOR]

In a recent study, Maheu et al. (Int J Forecast 36: 570–587, 2020) suggest a predictive regression model, where besides the conditional mean, the lagged value of the predictor of interest can also impact the dependent variable through the conditional volatility process. Their out-of-sample study focusing on predicting the conditional distribution of the US real GDP growth rate by conditioning on the price of crude oil finds strong evidence in favor of the suggested specification with respect to density forecast accuracy. In this study, we demonstrate that their framework is also very useful with regard to predicting aggregate equity returns by conditioning on macroeconomic variables. Using the well-known Goyal and Welsh dataset, we show that the suggested framework results in statistically significant more accurate density predictions relative to the stochastic volatility benchmark as well as competitors, where the lagged value of the predictor of interest impacts aggregate equity returns exclusively through the conditional mean process. Evidence of statistical predictability also results in VaR accuracy gains. [ABSTRACT FROM AUTHOR]

We describe the package MSGARCH, which implements Markov-switching GARCH (generalized autoregressive conditional heteroscedasticity) models in R with efficient C++ object-oriented programming. Markov-switching GARCH models have become popular methods to account for regime changes in the conditional variance dynamics of time series. The package MSGARCH allows the user to perform simulations as well as maximum likelihood and Bayesian Markov chain Monte Carlo estimations of a very large class of Markov-switching GARCH-type models. The package also provides methods to make single-step and multi-step ahead forecasts of the complete conditional density of the variable of interest. Risk management tools to estimate conditional volatility, value-at-risk, and expected-shortfall are also available. We illustrate the broad functionality of the MSGARCH package using exchange rate and stock market return data.

The paper provides an updated evidence of the linkage between stock market and macroeconomic factors in Pakistan. The sample period is from January 2011 to November 2017. Macroeconomic variables used are money supply, exchange rate, treasury bill rate, inflation and industrial production. Generalized autoregressive conditional heteroscedasticity (GARCH) models have been used to examine the impact of macroeconomic factors on stock market return and stock market volatility. Findings suggest that macroeconomic factors have an impact on stock market volatility. The fluctuations in inflation and money supply negatively influence the volatility of stock market returns. In contrast, industrial production positively affects the fluctuations of stock market returns. The findings are important for shareholders, investors, regulatory authorities and policymakers. [ABSTRACT FROM AUTHOR]

This paper aims to study the impacts of long memory in conditional volatility and conditional non-normality on market risks in Bitcoin and some other cryptocurrencies using an Autoregressive Fractionally Integrated GARCH model with non-normal innovations. Two tail-based risk metrics, namely Value at Risk (VaR) and Expected Shortfall (ES), are adopted to study the tail behaviour of market risks in Bitcoin and some other cryptocurrencies. Empirical investigations for the tail behaviour based on real exchange rate data of cryptocurrencies are conducted. An extreme-value-theory-based approach is used to study potential improvements in the estimation for the risk metrics under GARCH-type models. The possibility of explosive regimes in cryptocurrencies' volatilities is examined using Markov-switching GARCH models. [ABSTRACT FROM AUTHOR]

Forecasting and adequately measuring equity returns volatility is crucial for portfolio selection and trading strategies. Implied volatility is often considered to be informationally superior to the realized volatility. When available, implied volatility is largely used by practitioners and investors to forecast future volatility. To this extent we want to identify the best approach to track equity returns implied volatility using parametric and ANN approaches. Using daily equity prices and stock market indices traded on major international Exchanges we estimate time varying volatility using the E-GARCH approach, the Heston model and a novel ANN framework to replicate the corresponding implied volatility. Overall the ANN approach results the most accurate to track the equity returns implied volatility. [ABSTRACT FROM AUTHOR]

We estimated the stock market risk premium during the COVID-19 pandemic with a GARCH-in-Mean (GARCH-M)(1,1) model. The analysis then explored the presence of regime changes using a two-regime Markov-Switching GARCH (MS GARCH)(1,1) model. The sample we used included the stock market indexes of nine countries from three geographical regions, including: North America (Canada, USA, and Mexico), South America (Brazil and Argentina), and Asia (Japan, South Korea, Hong Kong, and Singapore), over two periods: (a) pre-COVID (from 1 January 2015 to 31 December 2019); and (b) COVID (from 1 January 2020 to 31 December 2021). Our GARCH-M(1,1) estimation results indicate that the more developed countries’ stock markets experienced an important increase in their risk premium during the COVID period, likely explained by the massive government anticyclical policies. By contrast, developing countries’ stock markets, particularly in Latin America, experienced a reduction, and in some cases, even a total loss of the risk premium effect. From the perspective of investors and portfolio risk managers, the identification of high and low volatility periods and their estimated probability of occurrence is useful for the characterization of stress scenarios and the design of emerging strategies. For governments and central bankers, the implementation of different policies should respond to the more likely scenarios but should also be prepared to respond to other less likely scenarios. Institutional preparedness to respond to as many different scenarios as may be identified with the use of MS GARCH models can make their interventions more successful. This work presents an objective example of how the use of MS GARCH models may be of use to practitioners in both the financial industry and government. We confirmed that the results of a two-regime MS GARCH model are superior to those obtained from a single-regime model.

This paper proposes the use of a spliced distribution with generalized Pareto tail for financial risk management. The proposed distribution is tailored to flexibly capture the heavy tail in asset return distribution. The parameters of the distribution can be estimated jointly with a conditional heteroskedasticity model. The estimated parameters can then be used to produce tail risk forecasts for risk management purposes. The use of the proposed distribution is illustrated by evaluating tail risk forecasts for a number of major stock indices. [ABSTRACT FROM AUTHOR]

This paper is concerned with model averaging estimation for conditional volatility models. Given a set of candidate models with different functional forms, we propose a model averaging estimator and forecast for conditional volatility, and construct the corresponding weight‐choosing criterion. Under some regulatory conditions, we show that the weight selected by the criterion asymptotically minimizes the true Kullback–Leibler divergence, which is the distributional approximation error, as well as the Itakura–Saito distance, which is the distance between the true and estimated or forecast conditional volatility. Monte Carlo experiments support our newly proposed method. As for the empirical applications of our method, we investigate a total of nine major stock market indices and make a 1‐day‐ahead volatility forecast for each data set. Empirical results show that the model averaging forecast achieves the highest accuracy in terms of all types of loss functions in most cases, which captures the movement of the unknown true conditional volatility. [ABSTRACT FROM AUTHOR]

This article aims to exhibit and study the impacts that changing characteristics of a fixed exchange rate regime has on conditional volatility. To do so, using the U.S. dollar dirham (USDMAD) daily closing rates over 23 years, we compare the GARCH model results of four segmented sub-periods to each other and then to the global period of the study to detect disparities. The main result is that changes in exchange rate regime characteristics do impact the conditional volatility. Therefore, we recommend that the study of conditional volatility should use periods with no changes in the characteristics of the exchange rate regime to avoid bias. Otherwise, the use of segmented sub-periods should be adopted to take account of these changes. Finally, we present some key results about the impacts of these changes in Morocco's exchange rate regime on the conditional volatility. [ABSTRACT FROM AUTHOR]

The leverage effect refers to the well-known relationship between returns and volatility for an equity. When returns fall, volatility increases. We evaluate the role of the leverage effect with regards to generating density forecasts of equity returns using well-known observation and parameter-driven conditional volatility models. These models differ in their assumptions regarding: The parametric specification, the evolution of the conditional volatility process and how the leverage effect is specified. The ability of a model to generate accurate density forecasts when the leverage effect is incorporated or not as well as a comparison between different model-types is analyzed using a large number of financial time series. For each model type, the specification with the leverage effect tends to generate more accurate density forecasts than its no-leverage counterpart. Among the specifications considered, the Beta-t-EGARCH model is the top performer, regardless of whether we attach the same weight to each region of the conditional distribution or emphasize the left tail. [ABSTRACT FROM AUTHOR]

In this study, the volatility of the BIST Bank (XBANK) index was tried to be modeled by using the conditional variance models GARCH, TGARCH and EGARCH. The XBANK Index daily closing values for 2010-2016 were obtained from the Thompson Reuters-Eikon database and used in the study. This period was adopted at first step to be able to exclude the effect of considerable changes in some of the indicators after 2016. By the obtained data, the logarithmic return series of the Banking Index was calculated during the period covered and GARCH (1,1), TGARCH (1,1) and EGARCH (1,1) models were established to calculate the index return volatility. The models are examined, a suitable model is determined and the volatility calculation is performed with the help of the conditional variance obtained from the appropriate model GARCH (1,1). [ABSTRACT FROM AUTHOR]