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Volatility is a permanent behavior of the stock market around the globe. The presence of the volatility in the stock price makes it possible to earn abnormal profits by risk seeking investors and creates hesitancy among risk averse investors as high volatility means high return with high risk. Investors always consider market volatility before making any investment decisions. Random fluctuations are termed as volatility of stock market. Volatility in financial markets is reflected because of uncertainty in the price and return, unexpected events and non-constant variance that can be measured through the generalized autoregressive conditional heteroscedasticity family models and that will give an insight for investment decision-making.

Daily data of the closing value of Bombay Stock Exchange (BSE) (Sensex) and National Stock Exchange (NSE) (Nifty) from April 1, 2011 to March 31, 2017 is collected through the web-portal of BSE (www.bseindia.com) and NSE (www.nseindia.com) for the analysis purpose.

The outcome of the study suggested that P-GARCH model is most suitable to predict and forecast the stock market volatility for both the markets.

Future research can be extended to other stock market segments and sectoral indices to explore and forecast the volatility to establish a trade-off between risk and return.

The results of previous studies available are not conducive to this research, and very limited scholarly work is available in the Indian context, so required to be re-explored to identify the appropriate model to predict market volatility.

The nexus of commodity prices with inflation is one of the main concerns for a nation's economy like India. The literature does not have enough volatility-based study, especially using the multivariate GRACH family of models to find a link between these two. It is the main reason for the conduct of this study. This paper aims to estimate the volatility effects of commodity prices on inflation.

For ten years (2011–2022), future prices of selected seven agriculture commodities and inflation indices (wholesale price index [WPI] and consumer price index [CPI]) are gathered every month. BEKK GARCH model (BGM) and DCC GARCH model (DGM) are employed to determine the volatility effect of commodity prices (CPs) on inflation.

The authors find that volatility's short-term (shock) impact on agricultural CPs to inflation does not exist. However, the long-term volatility spillover effect (VSE) is significant from commodities to inflation.

The study's findings have a significant implication for the policymakers to take a long-term view on inflation management regarding commodity prices. The findings can facilitate policy on the choice of commodities and the flexibility of their trading on the commodities derivatives market.

The findings of the study are unique. The authors do not observe any study on the volatility effect of agri-commodities (agricultural commodities) prices on inflation in India. This paper applies advanced techniques to provide novel and reliable evidence. Hence, this research is believed to contribute significantly to the knowledge body through its novel evidence and advanced approach.

Several empirical studies have proven that emerging countries are attractive destinations for Foreign Institutional Investors (FIIs) because of high expected returns, weak market efficiency and high growth that make them attractive destination for diversification of funds. But higher expected returns come coupled with high risk arising from political and economic instability. This study aims to compare the linear (symmetric) and non-linear (asymmetric) Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in forecasting the volatility of top five major emerging countries among E7, that is, China, India, Indonesia, Brazil and Mexico.

The volatility of financial markets of five major emerging countries has been empirically investigated for a period of two decades from January 2000 to December 2019 using univariate volatility models including GARCH 1, 1, Exponential Generalized Autoregressive Conditional Heteroscedasticity (E-GARCH 1, 1) and Threshold Generalized Autoregressive Conditional Heteroscedasticity (T-GARCH-1, 1) models. Further, to examine time-varying volatility, the distinctions of structural break have been captured in view of the global financial crisis of 2008. Thus, the period under the study has been segregated into pre- and post-crisis, that is, January 2001–December 2008 and January 2009–December 2019, respectively.

The findings indicate that GARCH (1, 1) model is superior to non-linear GARCH models for forecasting volatility because the effect of leverage is insignificant. China has been considered as most volatile, whereas India is volatile but positively skewed and Indonesia is the least volatile country. The results can help investors in better international diversification of their portfolio and identifying best suitable hedging opportunities.

This study can help investors to construct a more risk-adjusted returns international portfolio. Further, it adds to the scant literature available on the inconclusive debate on the choice of linear versus non-linear models to forecast market volatility.

Earlier studies related to univariate volatility models are mostly applications of the models. Only few studies have considered the robustness while applying the models. However, none of the studies to the best of the authors’ searches have considered these models for identifying the diversification opportunity among the emerging countries. Hence, this study is able to derive diversification and hedging opportunities by applying wide ranges of the statistical applications and models, that is, descriptive, correlations and univariate volatility models. It makes the study more rigorous and unique compared to the previous literature.

The purpose of this study is to investigate the volatility and forecast accuracy of the Islamic stock market for the period 1999–2017. This period is characterized by the occurrence of several economic and political events such as the September 11, 2001, terrorist attack and the 2007–2008 global financial crisis.

This study constructs a new hybrid generalized autoregressive conditional heteroskedasticity (GARCH)-type model based on an artificial neural network (ANN). This model is applied to the daily Dow Jones Islamic Market World Index during the period June 1999–January 2017.

The in-sample results show that the volatility of the Islamic stock market can be better described by the fractionally integrated asymmetric power ARCH (FIAPARCH) approach that takes into account asymmetry and long memory features. Considering the out-of-sample analysis, this paper has applied a hybrid forecasting model, which combines the FIAPARCH approach and the ANN. Empirical results reveal that the proposed hybrid model (FIAPARCH-ANN) outperforms all other single models such as GARCH, fractional integrated GARCH and FIAPARCH in terms of all performance criteria used in the study.

The results have some implications for Islamic investors, portfolio managers and policymakers. These implications are related to the optimal portfolio diversification decision, the hedging strategy choice and the risk management analysis.

The paper develops a new framework that combines an ANN and FIAPARCH model that introduces two important features of time series, namely, asymmetry and long memory.

The study aims to analyze the interaction between macroeconomic uncertainty and stock market return and volatility for China and USA and tries to draw some invaluable inferences for the investors, portfolio managers and policy analysts.

Empirically the study uses GARCH family models to capture the time-varying volatility of stock market and macroeconomic risk factors by using monthly data ranging from 1995:M7 to 2018:M6. Then, these volatility series are further used in the multivariate VAR model to analyze the feedback interaction between stock market and macroeconomic risk factors for China and USA. The study also incorporates the impact of Asian financial crisis of 1997–1998 and the global financial crisis of 2007–2008 by using dummy variables in the GARCH model analysis.

The empirical results of GARCH models indicate volatility persistence in the stock markets and the macroeconomic variables of both countries. The study finds relatively weak and inconsistent unidirectional causality for China mainly running from the stock market to the macroeconomic variables; however, the volatility spillover transmission reciprocates when the impact of Asian financial crisis and Global financial crisis is incorporated. For USA, the contemporaneous relationship between stock market and macroeconomic risk factors is quite strong and bidirectional both at first and second moment level.

This study investigates the interaction between stock market and macroeconomic uncertainty for China and USA. The researchers believe that none of the prior studies has made such rigorous comparison of two of the big and diverse economies (China and USA) which are quite contrasting in terms of political, economic and social background. Therefore, this study also tries to test the presumed conception that macroeconomic uncertainty in China may have different impact on the stock market return and volatility than in USA.

The paper aims to analyse the extent of volatility and generating forecasts of exchange rates of British pound and Indian rupees in US terms.

This study applies different combinations of GARCH and EGARCH models suggested in the Econometric literature to capture the extent of volatility. The forecast of exchange rates of British Pound and Indian Rupees in US terms are generated applying artificial neural network (ANN) technique using different combination of networks with hyperbolic tangent function at hidden and output stage of the model.

The presence of volatility depicts that there is noise and chaos in the forex market. Prediction of exchange rate of the respective currencies underscores that exchange rates will increase marginally in near future.

The results proposed in this study will be benchmark for the hedgers, investors, bankers, practitioners and economists to foresee the exchange rate in the presence of volatility and design policies accordingly.

In literature, no study has applied ANN for forecasting exchange rate after measuring the extent of volatility. The present study is a unique contribution in the existing pool of literature to forecasts the concerned variable(s) after ascertaining the noise and chaos in the data by applying GARCH family models.

The purpose of this study is to investigate the performance of Value-at-Risk (VaR) models for nine Middle East and North Africa Islamic indices using RiskMetrics and VaR parametric models.

The authors test the performance of several VaR models using Kupiec and Engle and Manganelli tests at 95 and 99 per cent levels for long and short trading positions, respectively, for the period from August 10, 2006 to December 14, 2014.

The authors’ findings show that the VaR under Student and skewed Student distribution are preferred at a 99 per cent level VaR. However, at 95 per cent level, the VaR forecasts obtained under normal distribution are more accurate than those generated using models with fat-tailed distributions. These results suggest that VaR is a good tool for measuring market risk. The authors support the use of RiskMetrics during calm periods and the asymmetric models (Generalized Autoregressive Conditional Heteroskedastic and the Asymmetric Power ARCH model) during stressed periods.

These results will be useful to investors and risk managers operating in Islamic markets, because their success depends on the ability to forecast stock price movements. Therefore, because a few Islamic financial institutions use internal models for their capital calculations, the regulatory committee should enhance market risk disclosure.

This study contributes to the knowledge in this area by improving our understanding of market risk management for Islamic assets during the stress periods. Then, it highlights important implications regarding financial risk management. Finally, this study fills a gap in the literature, as most empirical studies dealing with evaluating VaR prediction models have focused on quantifying the model risk in the conventional market.

This paper aims to analyze the characteristics of stochastic volatility processes in globally listed private equity (LPE) markets, which are represented by nine global, regional and style indices, and reveals transmissions in the conditional variances between the different markets, based on weekly data covering the period January 2011 to December 2020.

The study uses the generalized autoregressive conditional heteroscedasticity [GARCH(p, q)] model and its exponential GARCH (EGARCH) and GARCH-in-mean extensions.

The estimates of the volatility models GARCH, EGARCH and GARCH-in-mean GARCH-M for testing the stylized properties persistence, asymmetry, mean reversion and risk premium lead to very different results, depending on the respective LPE index.

The knowledge of conditional volatilities of LPE returns as well as the detection of volatility transmissions between the different LPE markets under investigation serve to support asset allocation decisions with respect to risk management or portfolio allocation. Hence, the findings are important for all kinds of investors and asset managers who consider investments in LPE.

The authors present a novel study that examines the conditional variance for globally LPE markets by using LPX indices, offering valuable insight into this growing asset class.

This paper investigates the influence of the ongoing crisis of Russia's incursion on Ukraine on the risk dynamics of energy futures contracts with high-frequency data on four different futures contracts using risk metrics of value at risk (VaR) and conditional value at risk (CVaR) for the USA market.

The author used different generalised autoregressive conditional heteroscedasticity - Extreme Value Theory (GARCH)-EVT models and compared the performance of each of the competing models. Backtesting evidence shows that VaR and CVaR combined with GARCH-EVT better estimate risk.

The study results show that combined risk metrics are efficient and adaptive to estimating the risk dynamics and backtesting of the models, revealing that the autoregressive moving average (ARMA) (1,1)-asymmetric power autoregressive conditional heteroscedasticity (APARCH) model performs relatively better than other models.

The paper has practical implications for different market participants. From the risk manager's and day traders' angles, the market participants can estimate the risk exposure in the energy futures contract and take positions accordingly. The results are important for oil-importing countries due to the developing supply crisis and price escalation, which can brew inflation in the economy.

To the best of the author's knowledge, the paper is the first to throw light on the risk angle of energy futures contracts during the ongoing crisis of the Russia–Ukraine war.

To study stochastic volatility in the pricing of options.

Random‐coefficient autoregressive and generalized autoregressive conditional heteroscedastic models are studied. The option‐pricing formula is viewed as a moment of a truncated normal distribution.

Kurtosis for RCA and for GARCH process is derived. Application of random coefficient GARCH kurtosis in analytical approximation of option pricing is discussed.

Findings are useful in financial modeling.