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The purpose of the article is to analyze the relevance of earnings fundamentals in predicting extreme price reversals of an emerging stock market. We collect monthly price data on six sector indices from Bombay Stock Exchange (BSE) of India for the period 2004–2019. The research decomposes industry stock returns into Potential Maximum Gains (PMG) and Potential Maximum Losses (PML) with price extremes at first and then tests price reversal behavior using Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) and vector autoregressive (VAR) models. The study finds symmetry between PMG and PML in the banking, realty, and oil sectors, while the asymmetric reversal behavior is noted in the automobiles and capital goods industries. The presence of industry fundamentals in the models estimating the reversal behavior of share prices enhances their predictive power, which suggests the significance of value strategies in making gains from extreme price variations. The price reversal behavior is sector specific and found inconsistent in emerging market. Hence, the investors cannot overlook the relevance of the industry characteristics and earnings fundamentals while predicting the stock price behavior in emerging markets. [ABSTRACT FROM AUTHOR]

Aggregated long and short trading risk positions of speculative assets over time are likely to be unequal. This may be because of irrational decisions of traders and investors as well as catastrophic events that lead to pronounce or salient market crashes. Returns of such assets are therefore more likely to have one polynomial tail and one exponential tail. The generalized hyperbolic (GH) skewed Student‐t distribution is known to handle such situations quite well. In this paper, we use generalized autoregressive conditional heteroscedasticity (GARCH) models to empirically show the superiority of the GH skewed Student‐t distribution in forecasting the extreme tail risks of cryptocurrency returns in the presence of substantial skewness in comparison with some competing distributions. Furthermore, we show the practical significance of the GH skewed Student‐t distribution‐based risk forecasts in computing daily capital requirements. Evidence from the study suggests that the GH skewed Student‐t distribution model tends to be superior in forecasting volatility and expected shortfall (ES) but not value‐at‐risk. In addition, the distribution yields higher value‐at‐risk (VaR) exceptions but surprisingly avoids the red zone of the Basel II accord penalty zones and produces lower but optimal daily capital requirements. Therefore, in the presence of substantially skewed returns having exponential‐polynomial tails, we recommend the use of the GH skewed Student‐t distribution for parametric GARCH models in forecasting extreme tail risk. [ABSTRACT FROM AUTHOR]

Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat‐tailed and heteroscedastic with regime switching dynamic correlations. The conditional return distribution is modeled by an elliptical multi‐variate generalized hyperbolic distribution, allowing for fast parameter estimation via an expectation‐maximization algorithm, and a semi‐closed form of the risk contributions. A new method for efficient computation of non‐Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish–Fisher‐type approximations. Accounting for fat‐tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis or the COVID shock. While risk parity portfolios are rather robust to the misuse of the Gaussian distribution, a sophisticated time series model can improve risk‐adjusted returns, strongly reduces drawdowns during periods of market stress and enables to use a holistic risk model for portfolio and risk management. [ABSTRACT FROM AUTHOR]

The purpose of this research is to investigate the use of cross-hedging in the South African soybean market, by using the JSE BEAN contract as a cross-hedge instrument for the JSE SOYA contract. The research study involves a detailed assessment of the data, which includes the use of stationarity tests such as the Phillips-Perron and Augmented Dickey-Fuller, as well as the Johansen co-integration approach to analyse long-term relationships between the variables. To evaluate the efficiency of cross-hedging strategies, three distinct hedging models are used: the ordinary least squares (OLS) model, error correction model (ECM) and EC-GARCH. The results demonstrate that these models produce significant hedge ratios. Through back-testing and the application of hedging strategies, it is determined that the JSE BEAN contract holds the potential to serve as a cross-hedge for the JSE SOYA contract in the South African soybean market. This study provides useful information for market participants and model selection in the context of cross-hedging. [ABSTRACT FROM AUTHOR]

The objective of this article is to examine the volatility spillover effect between the foreign exchange market and the stock market of Brazil, Russia, India, China and South Africa (BRICS) countries along with Japan as the developed country in the region, affecting the BRICS countries. Generalized Autoregressive Conditionally Heteroscedastic (GARCH) (1,1) method is used to study the volatility between the stock market and the foreign exchange market in selected countries, and asymmetric model, that is, Exponential Generalized Autoregressive Conditional Heteroscedasticity—EGARCH (1,1) is also used to investigate the presence of leverage effects in both stock market and foreign exchange market in selected countries. GARCH findings suggest a two-way volatility spillover between the stock market and foreign exchange markets for India, China and South Africa. In BRICS countries, volatility spillover from the currency market to the stock market is seen as more evident and robust as compared to spillover from the stock market to the currency market. A positive asymmetry in spillover is also observed from the foreign exchange market to the stock market. The findings of the study may provide valuable information to investors for decision-making in international portfolio investment and also for economic policymakers for their financial stability perspective. [ABSTRACT FROM AUTHOR]

The growing interest in cryptocurrencies has brought this new means of exchange to the attention of the financial world. This study aims to investigate the effects that a cryptocurrency can have when it is considered as a financial asset. The analysis is carried out from an ex‐post perspective, evaluating the performance achieved in a certain period by three different portfolios. These are the one composed only of equities, bonds and commodities, the second one only of cryptocurrencies, and the third one is a combination of these both ones and thus made up of all considered "traditional" assets and the most performing cryptocurrency of the second portfolio. For these purposes, the classic variance‐covariance approach is applied where the calculation of the risk structure is done via the GARCH‐Copula and GARCH‐Vine Copula approaches. The optimal weights of the assets in the optimized portfolios are determined through Markowitz optimization problem. The analysis mainly showed that the portfolio composed of cryptocurrency and traditional assets has a higher Sharpe index, from an ex‐post perspective, and more stable performances, from an ex‐ante perspective. We justify our selection of the Markowitz approach over conditional VaR and expected shortfall due to their heightened sensitivity to unsystematic extreme events in crypto markets. [ABSTRACT FROM AUTHOR]

We present novel, robust methods for inference on market (non-)efficiency, volatility clustering, and nonlinear dependence in financial return series. In contrast to existing methodology, our proposed methods are robust against nonlinear dynamics and tail-heaviness of returns. Specifically, our methods only rely on return processes being stationary and weakly dependent (mixing) with finite moments of a suitable order. This includes robustness against power-law distributions associated with nonlinear dynamic models such as GARCH and stochastic volatility. The methods are easy to implement and perform well in realistic settings. We revisit a recent study by Baltussen, van Bekkum, and Da (2019 , J. Financ. Econ. , 132, 26–48) on autocorrelation in major stock indexes. Using our robust methods, we document that the evidence of the presence of negative autocorrelation is weaker, compared with the conclusions of the original study. [ABSTRACT FROM AUTHOR]

We study two sources of heteroscedasticity in high-frequency financial data and estimate their contribution to overall volatility by means of a Markov switching (MS) structural VAR model. We achieve identification for all coefficients by assuming that the structural errors follow a GARCH-DCC process. Using transaction data of the EUR/USD interdealer market in 2016, we first detect three regimesof volatility. Then we show that both sources of volatility matter for the transmission of shocks, and that information is channeled to the market mostly through demand shocks. This suggests that, on the EUR/USD market, some liquidity takers (LTs) are better informed than both liquidity providers and those LTs who follow a feedback strategy. [ABSTRACT FROM AUTHOR]

ABSTRACT Precious metals are rare metals with high economic value. Forecasting the price volatility of precious metals is essential for investment purposes. In this work, we propose a novel hybrid model of random convolutional kernels‐based neural network model (RCK) and generalized autoregressive conditional heteroscedasticity (GARCH) model for forecasting the metal price volatilities of gold, silver, and platinum. Realized volatility calculated on logarithmic returns is used as an estimate for the volatility of prices, and data standardization is performed before feeding the price volatility data to the RCK model. RCK model applies multiple carefully designed random convolution kernels on the time series input to extract robust features for forecasting. The proportion of positive values (PPV) is extracted as features from the output of convolving convolutional kernels with time‐series inputs, which are then passed through a regressor to forecast volatility. Compared to the existing methods, the proposed method has the advantage that the weights of the random convolutional kernels need not be trained, unlike other neural network models. Further, no other work has made use of random convolutional kernels for precious metal forecasting, to the best of our knowledge. We incorporated novel learning and data augmentation strategies to achieve better performance. In particular, we used the cosine annealing learning rate strategy and Mixup data augmentation technique to improve the proposed model's performance. We have used MSE (Mean Squared Error), RMSE (Root Mean Squared Error), MAE (Mean Absolute Error), and MAPE (Mean Absolute Percentage Error) as metrics to compare the proposed models' performance. The proposed model decreases the MSE by 53% compared to the GARCH‐LSTM model, which is the current state‐of‐the‐art hybrid model for volatility forecasting. [ABSTRACT FROM AUTHOR]

This study investigated the impact of exchange rate volatility on sectoral stock volatility by employing the intraday volatility measure directly calculated from the original data, using daily data from 27 Borsa Istanbul sectors between April 29, 2003, and April 25, 2023. In the literature, GARCH models are commonly used to study the volatility spillovers between exchange rates and stock prices, typically using aggregate data. However, the GARCH family models provide inefficient and biased estimates if they are misspecified. Moreover, using aggregate-level data may lead to biased and misleading conclusions. The research used intraday volatility measures to overcome the shortcomings of GARCH models. The ordinary least squares (OLS), GARCH (1,1) methods, and Garman and Klass (1980) volatility estimator are used. The empirical results showed that the estimates from each method vary significantly, and these disparities in the results might be due to misspecification in GARCH (1,1) models. The intraday volatility model estimation results showed that although stock price volatilities in all sectors are positively and significantly affected by exchange rate volatility, their magnitudes vary significantly. Taken together, this implies the presence of vast heterogeneities in the responses of sectoral stock price volatilities to exchange rate volatility. The results encourage policymakers to pay special attention to these heterogeneities to prevent capital flights and underinvestment. Additionally, the findings assist investors in making more effective decisions by helping them adapt their investment strategies to factor in exchange rate fluctuations and mitigate the impact of unexpected events in the exchange rate market. [ABSTRACT FROM AUTHOR]

The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO2 emissions in addition to examining these series for entropy, long-range dependence, fractionality, complexity, chaos, and nonlinearity with a dataset spanning from 25 June 2012 to 22 June 2024. Empirical results from Shannon, Rényi, and Tsallis entropy measures; Kolmogorov–Sinai complexity; Hurst–Mandelbrot and Lo's R/S tests; and Phillips' and Geweke and Porter-Hudak's fractionality tests confirm the presence of entropy, complexity, fractionality, and long-range dependence. Further, the largest Lyapunov exponents and Hurst exponents confirm chaos across all series. The BDS test confirms nonlinearity, and ARCH-type heteroskedasticity test results support the basis for the use of novel TAR-TR-GARCH–copula causality. The model estimation results indicate moderate to strong levels of positive and asymmetric tail dependence and contagion under distinct regimes. The novel method captures nonlinear causality dynamics from Bitcoin and Fintech to energy consumption and CO2 emissions as well as causality from energy consumption to CO2 emissions and bidirectional feedback between Bitcoin and Fintech. These findings underscore the need to take the chaotic and complex dynamics seriously in policy and decision formulation and the necessity of eco-friendly technologies for Bitcoin and Fintech. [ABSTRACT FROM AUTHOR]

Accurate risk assessment is crucial for predicting potential financial losses. This paper introduces an innovative approach by employing expected risk models that utilize risk samples to capture comprehensive risk characteristics. The innovation lies in the integration of classical credibility theory with expected risk models, enhancing their stability and precision. In this study, two distinct expected risk models were developed, referred to as Model Type I and Model Type II. The Type I model involves independent and identically distributed random samples, while the Type II model incorporates time-varying stochastic processes, including heteroscedastic models like GARCH(p,q). However, these models often exhibit high variability and instability, which can undermine their effectiveness. To mitigate these issues, we applied classical credibility theory, resulting in credible expected risk models. These enhanced models aim to improve the accuracy of Value-at-Risk (VaR) forecasts, a key risk measure defined as the maximum potential loss over a specified period at a given confidence level. The credible expected risk models, referred to as CreVaR, provide more stable and precise VaR forecasts by incorporating credibility adjustments. The effectiveness of these models is evaluated through two complementary approaches: coverage probability, which assesses the accuracy of risk predictions; and scoring functions, which offer a more nuanced evaluation of prediction accuracy by comparing predicted risks with actual observed outcomes. Scoring functions are essential in further assessing the reliability of CreVaR forecasts by quantifying how closely the forecasts align with the actual data, thereby providing a more comprehensive measure of predictive performance. Our findings demonstrate that the CreVaR risk measure delivers more reliable and stable risk forecasts compared to conventional methods. This research contributes to quantitative risk management by offering a robust approach to financial risk prediction, thereby supporting better decision making for companies and financial institutions. [ABSTRACT FROM AUTHOR]

This study rigorously investigates the impact of COVID-19 on Tunisian stock market volatility. The investigation spans from January 2020 to December 2022, employing a GJR-GARCH model, bias-corrected wavelet analysis, and an ARDL approach. Specific variables related to health measures and government interventions are incorporated. The findings highlight that confirmed and death cases contribute significantly to the escalation in TUNINDEX volatility when using both the conditional variance and the realized volatility. Interestingly, aggregate indices related to government interventions exhibit substantial impacts on the realized volatility, indicating a relative resilience of the Tunisian stock market amidst the challenges posed by COVID-19. However, the application of the bias-corrected wavelet analysis yields more subtle outcomes in terms of the correlations of both measures of volatility to the same metrics. Our econometric implications bear on the application of such a technique, as well as on the use of the realized volatility as an accurate measure of the "true" value of volatility. Nevertheless, the measures and actions undertaken by the authorities do not exclude fear and insecurity from investors due to another virus or any other crisis. The positive and long-term impact on the volatility of US equity market uncertainty, VIX, economic policy uncertainty (EPU), and the infectious disease EMV tracker (IDEMV) is obvious through the autoregressive distributed lag model (ARDL). A potential vulnerability of the Tunisian stock market to future shocks is not excluded. Government and stock market authorities should grapple with economic and financial fallout and always instill investor confidence. Importantly, our results put mechanisms such as overreaction to public news and (in)efficient use of information under test. Questioning the accuracy of announcements is then recommended. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this study is to investigate the impact of terrorist attacks on the volatility and returns of the stock market in Tunisia. Design/methodology/approach – The employed sample comprises 1250 trading day from the Tunisian stock index (Tunindex) and stock closing prices of 64 firms listed on the Tunisian stock market (TSM) from January 2011 to October 2015. The research opts for the general autoregressive conditional heteroscedasticity (GARCH) and exponential generalized conditional heteroscedasticity (EGARCH) models framework in addition to the event study method to further assess the effect of terrorism on the Tunisian equity market. Findings – The baseline results document a substantive impact of terrorism on the returns and volatility of the TSM index. In more details, the findings of the event study method show negative significant effects on mean abnormal returns with different magnitudes over the events dates. The outcomes propose that terrorism profoundly altered the behavior of the stock market and must receive sufficient attention in order to protect the financial market in Tunisia. Originality/value – Very few evidence is found on the financial effects of terrorism over transition to democracy cases. This paper determines the salient reaction of the stock market to terrorism during democratic transition. The findings of this study shall have relevant implications for stock market participants and policymakers.

Numerous scholars have examined the relationship between stock returns and metal commodities, but there has been less emphasis on specific metal commodities such as coal and nickel. This study sought to investigate the correlation between coal and nickel price fluctuations and their impact on stock market volatility. The researchers employed the GARCH and EGARCH models for analysis. This study utilized data on coal price, nickel price, and two stock market indices in Indonesia, specifically LQ45 and IDX30, spanning from January 2020 to December 2023. The results indicate that there was no substantial correlation between coal shock and nickel shock on stock market volatility. The EGARCH model would be more suitable for prediction. The significance of this research lies in its discovery of the relationship between coal shock and nickel shock on stock return throughout a dynamic period.

Risk and volatility are two related factors in research regarding capital markets. Many factors influence the movement of shares and indices. Volatility is common and affects risk assessment. Stock price volatility is an important aspect of understanding market behavior, with high volatility reflecting rapid and unstable price fluctuations. This research investigates the GARCH model in assessing volatility on the IBM Stock Exchange. The method employed was the symmetric GARCH model. It focuses on univariate analysis using the GARCH econometric model. The GARCH model allows modeling stock price variance over time based on the assumption that the variance was influenced by past stock price variance. The stages of this research were (1) data collection, (2) data pre-processing, and (3) forecasting model implementation. The best model obtained was ARMA(4,2)-GARCH(5,6) with an AIC value of 4.1017. A lower AIC value indicates that the model explains the data better or more optimally. A diagnostic test found that the model was adequate because the residual distribution followed a straight line, which means it was normally distributed.

In this paper, the autoregressive distributive lag (ARDL) model is used to examine the impact of global crude oil price on manufacturing output in India and the behaviour of consumer price index. Error correction model, co-integration and multivariate GARCH model models are used for the analysis. ARDL analysis shows a significant relation between consumer price index (CPI) and manufacturing index (MI). Also, a significant inverse relation is established between crude oil price with MI and a positive relation between MI and CPI. Despite an inconsistent short run relation between petrol price with CPI, rising fuel price shows dampening impact on manufacturing output in the long run.

Using ‘working’ assumptions on conditional third and fourth moments of errors, we propose a method of moments estimator that can have improved efficiency over the popular Gaussian quasi‐maximum likelihood estimator (GQMLE). Higher‐order moment assumptions are not needed for consistency – we only require the first two conditional moments to be correctly specified – but the optimal instruments are derived under these assumptions. The working assumptions allow both asymmetry in the distribution of the standardized errors as well as fourth moments that can be smaller or larger than that of the Gaussian distribution. The approach is related to the generalized estimation equations (GEE) approach – which seeks the improvement of estimators of the conditional mean parameters by making working assumptions on the conditional second moments. We derive the asymptotic distribution of the new estimator and show that it does not depend on the estimators of the third and fourth moments. A simulation study shows that the efficiency gains over the GQMLE can be non‐trivial. [ABSTRACT FROM AUTHOR]

This paper investigates five different Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Condition-al Heteroscedacity (GARCH models (GARCH, exponential GARCH or EGARCH, integrated GARCH or IGARCH, Component GARCH or CGARCH and the Glosten-Jagannathan-Runkle GARCH or GJR-GARCH) along with six distributions (normal, Student's t, GED and their skewed forms), which are used to estimate the price dynamics of the Bulgarian stock index SOFIX. We use the best model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data cover the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at analysing the SOFIX price and which distribution is most appropriate. The results, based on the BIC and AIC, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student's t-distribution is preferred for modelling. From the results obtained, we can confirm that the CGARCH model specification supports a more appropriate description of SOFIX volatility than a simple GARCH model. We find that long-term shocks have a more persistent impact on volatility than the effect of short-term shocks. Furthermore, for the same magnitude, negative shocks to SOFIX prices have a more significant impact on volatility than positive shocks. According to the results, when predicting future values of SOFIX, it is necessary to include both a first-order autoregressive component and a first-order moving average in the mean equation. With the help of 5000 simulations, it is estimated that the chances of SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087. [ABSTRACT FROM AUTHOR]

The high returns of cryptocurrencies have attracted many investors in recent years. At the same time the evolution of cryptocurrencies is characterized by extreme volatility. For investors, it is therefore key to gauge the risks related to an investment in cryptocurrencies. We provide a comparison of several GARCH and stochastic volatility models for forecasting the risk of cryptocurrencies over the out-of-sample period from 28.09.2018 to 28.02.2023. It turns out that the widely used GARCH(1,1) does not provide accurate risk predictions. In contrast, adding t-distributed innovations or allowing for regime changes improves the accuracy in both model classes. Finally, we consider a Bayesian decision-guided approach with discount learning to combine the different models and provide robust evidence that combining the model predictions leads to accurate combined risk predictions. [ABSTRACT FROM AUTHOR]

The literature documents that cultural factors affect housing or real estate markets and their interactions. Given this, we map global housing markets into different cultural blocs, and study the dynamics of price interaction among them. We investigate the extent and manner of price interaction within and between cultural blocs using a battery of econometric tests and network analyses. We confirm that housing markets within the same blocs are highly correlated, cointegrated and react to each other more quickly than those among different blocs. Our results provide a new perspective on the important role of culture in the transmission of linkages among housing markets globally and have vital implications for the global coordination of policies to stabilize housing markets. [ABSTRACT FROM AUTHOR]

Statistical process monitoring (SPM) offers an important toolkit used to monitor the stability of a process to improve the quality of outputs and/or services. More often, the design of control charts requires the estimation of the probability density function that involves selecting a common distribution that facilitates the estimation of the process parameters. The Bayesian approach is one of the most efficient techniques used in such instances. It incorporates informative and non-informative priors, i.e., uses information on past data and charting structures, to estimate parameters more efficiently than classical approaches. Bayesian approaches reduce the total expected cost over a finite horizon or the long-run expected average cost. This paper introduces a new Bayesian exponentially weighted moving average (EWMA) monitoring scheme for long runs based on an ARMA-GARCH model. The properties of the new monitoring scheme are investigated in terms of the run-length distribution. A case study on monitoring the USD to ZAR exchange rate is provided using the proposed Bayesian ARMA-GARCH EWMA monitoring scheme. [ABSTRACT FROM AUTHOR]

M-regression and quantile methods have been suggested to estimate generalized autoregressive conditionally heteroscedastic (GARCH) models. In this paper, we propose an M-quantile approach, which combines quantile and M-regression to obtain a robust estimator of the conditional volatility when the data have abrupt observations or heavy-tailed distributions. Monte Carlo experiments are conducted to show that the M-quantile approach is more resistant against additive outliers than M-regression and quantile methods. The usefulness of the method is illustrated on two financial datasets. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the downside risk of alternative investment funds (AIFs) in a cross-country setting over a period of 2015–2021, using popular Value-at-Risk (VaR henceforth) models, and test the efficacy of such models in capturing the volatility posed by these funds. We estimate VaR in the presence of three error distributions, including normal distribution, Student's t distribution, and GED distribution. Using weekly return data of 991 AIFs from 28 countries, over the period 2015–2021, we find that most of the funds, irrespective of country representation, exhibited a significant proportion of their weekly returns to be negative. To statistically validate our findings we use three backtesting approaches, i.e., Jorion's failure rate, Kupiec's proportion of failure (POF) tests and Christoffersen's independence test. Our findings indicate the presence of significant downside risk for AIFs, which these popular VaR models are unable to capture. These findings highlight the need for investors and fund managers to be cautious when relying solely on popular VaR models to manage downside risk in AIF and suggest that further research is needed to develop more effective risk management strategies for AIF, particularly in light of their complex structure and asymmetric return distributions. [ABSTRACT FROM AUTHOR]

This paper examines the effects of the COVID-19 pandemic on the volatility of the TUNINDEX stock market. Our main goal is to decipher how this worldwide health epidemic has influenced Tunisia's financial stability. A thorough empirical approach was employed, leveraging sophisticated econometric techniques such as GARCH and VECM to scrutinize daily market data. The analysis uncovers a notable escalation in TUNINDEX volatility during the pandemic, emphasizing the critical role of investors' sentiment, economic, and monetary interventions in mitigating the crisis. These insights shed light on the dilemmas and prospects facing investors, portfolio managers, and policymakers in navigating market volatility amidst pandemic uncertainty. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to test for volatility spillovers among Islamic stock markets with the exogenous impact of geopolitical risk (GPR) to check the risk transmission among Saudi Arabia, Malaysia, Indonesia and Turkey. Researchers test for both the symmetric and asymmetric risk transmission. Design/methodology/approach: For the symmetric response of volatility, the study uses simple generalized autoregressive conditional heteroscedastic (GARCH) and for the asymmetric response of volatility with the exogenous impact of GPR, the exponential GARCH models have been adopted. Findings: The results suggest spillover effects exist from Turkey to Saudi Arabia, Indonesia to Malaysia and Saudi Arabia and Malaysia to Indonesia. The findings of volatility spillover from GPR to sample countries suggest that only Malaysia and Indonesia experience volatility spillovers from GPR. Research limitations/implications: The present study is limited to the context of four countries and Islamic equities; the study contributes to the literature on volatility spillover, Islamic finance, GPR and asset pricing. Practical implications: This study contributes to individual, institutional investors' policymakers' knowledge in determining security prices, trading plans, investment hedging and policy regulation. Social implications: The extant literature disregards the GPR index to examine the volatility spillover effects among Islamic stock markets, which allow researchers to justify the mechanism of risk transmission due to GPR across the Islamic stock market. Originality/value: To the best of the authors' knowledge, this is the first research of its type to look at volatility spillover and GPR transmission in Islamic stock markets. [ABSTRACT FROM AUTHOR]

This paper investigates the estimation of the value at risk (VaR) across various probability levels for the log-returns of a comprehensive dataset comprising four thousand crypto-assets. Employing four recently introduced adaptive conformal inference (ACI) algorithms, we aim to provide robust uncertainty estimates crucial for effective risk management in financial markets. We contrast the performance of these ACI algorithms with that of traditional benchmark models, including GARCH models and daily range models. Despite the substantial volatility observed in the majority of crypto-assets, our findings indicate that ACI algorithms exhibit notable efficacy. In contrast, daily range models, and to a lesser extent, GARCH models, encounter challenges related to numerical convergence issues and structural breaks. Among the ACI algorithms, Fully Adaptive Conformal Inference (FACI) and Scale-Free Online Gradient Descent (SF-OGD) stand out for their ability to provide precise VaR estimates across all quantiles examined. Conversely, Aggregated Adaptive Conformal Inference (AgACI) and Strongly Adaptive Online Conformal Prediction (SAOCP) demonstrate proficiency in estimating VaR for extreme quantiles but tend to be overly conservative for higher probability levels. These conclusions withstand robustness checks encompassing the market capitalization of crypto-assets, time-series size, and different forecasting methods for asset log-returns. This study underscores the promise of ACI algorithms in enhancing risk assessment practices in the context of volatile and dynamic crypto-asset markets. [ABSTRACT FROM AUTHOR]

Bitcoin has gradually gained acceptance as a payment method that, unlike electronic payments in dollars or euros, passes through the international trading system with zero or lower fees. Moreover, Bitcoin and e-commerce have become increasingly intertwined in recent years as cryptocurrencies gain mainstream acceptance. In this paper, we analyze Bitcoin price evolution from September 2014 until July 2023, factors that influence price volatility and assess its future volatility using Autoregressive Conditional Heteroskedasticity (ARCH) models that predict the volatility of financial returns to conceive strategies for merchants that accept Bitcoin as a payment option. The Generalized ARCH model (GARCH) extends the model to capture more persistent volatility patterns. Further, we estimate symmetric and asymmetric GARCH (1,1)-type models with normal and non-normal innovations. The best proved to be EGARCH (1,1) with t-distribution innovation. To assist merchants in making decisions regarding Bitcoin adoption, two concepts are relevant: the EGARCH model and VaR. EGARCH model is used to forecast the volatility of the financial asset, while VaR is a widely used risk management tool that estimates the potential loss in value of a portfolio over a defined period. For a merchant holding Bitcoin, VaR assists in understanding the maximum expected loss over a certain time frame with a certain level of confidence (like 95% or 99%). The results show that a VaR coverage of 0.044 at a 5% probability level suggests that there is 95% confidence that the maximum loss will not exceed 4.4% of the investment value. [ABSTRACT FROM AUTHOR]

Abstract Focusing on the Russia–Ukraine war, this paper investigates natural gas futures volatilities. Applying several hybrid GARCH and EGARCH models, which innovatively incorporate both fat-tailed distribution errors and structural breaks, we derive the following new evidence. First, our hybrid modeling approach is effective in timely capturing the natural gas futures volatility spike when tensions simmered on the Russia–Ukraine border. Second, the hybrid modeling approach is effective for not only GARCH modeling but also EGARCH modeling. Third, the volatility estimates from our hybrid models have predictive power for the volatilities of nonhybrid models. Fourth, the volatility estimates from the nonhybrid models lag behind the volatilities of our hybrid models.

Recently, the interest of researchers in the use of hybrid models in the process of analyzing model time series with fluctuations and forecasting fluctuations in financial time series has increased significantly. Hybrid ARMA-GARCH models were created for medium- and long-term forecasts of time series of financial market index prices: ARMA models are used to analyze their linear component, which is a combination of autoregressive models and moving average models, and GARCH models are used to analyze the nonlinear component. which are generalized autoregressive models that depend on the nonconstancy of variance models. Hybrid ARMA-GARCH models eliminate the weaknesses and gaps that exist in each group of models (ARMA and GARCH) separately, which increases their forecasting accuracy and reliability, so they have already been successfully applied to model and forecast daily stock returns for three standard indices in the USA. The purpose of this article is to investigate which of the hybrid ARMA-GARCH models is optimal for forecasting the return of the DAX index, which is the most important stock index of the German securities market. It is the German equivalent of the American Dow Jones Index, has been calculated since 1988 by Deutsche Börse AG and reflects the total return on capital of the largest stock companies listed on the Frankfurt Stock Exchange (currently 40; by 2021 – 30): calculated as a weighted average of capitalization of the value of Free Float share prices on the Xetra electronic exchange, and also takes into account dividends on shares, assuming that the dividend is reinvested in the share on which it was accrued. The database of this study consisted of the daily closing prices of the DAX index presented on the official website of the Frankfurt Stock Exchange during the period from 01.01.2018 to 09.30.2023 (altogether about 1,500 observations), the stability of the time series was assessed using Expanded Dickey Fuller Liquidity (ADF). The article proposes 7 hybrid models, from which the one that is best suited for modeling the volatility of the DAX index is selected. It is an ARMA (2,3)-EGARCH (1,1) model because it captures volatility and leverage effects on DAX returns and its expected returns more than other models. The selection of the best alternative from the developed array of hybrid models was carried out according to the following criteria: AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), H-QIC (Hannan-Quinn Information Criterion).

Many investors and financial managers are interested in derivatives, which are financial instruments that derive their value from an underlying asset. These instruments have become popular due to their low initial requirements for futures trading and the need to pay premiums for options. The aim of this research, then, was to examine how the inclusion of Nifty index options impacts underlying market volatility using ARCH and GARCH models. The data set used in this study consists of 5996 time-series observations of NSE Nifty index closing prices. Here, the observations span from November 7, 1994, to December 31, 2018. Of these, 1622 observations are from the period before the introduction of options trading, while the remaining 4374 observations are from the period after the introduction of options trading. To determine the robustness of the study, the ARCH family has been chosen in order to capture the volatility behaviour and accommodate for heteroscedasticity in the returns. The coefficient’s negative sign suggests that the introduction of index options has a stabilised effect on underlying market volatility, even when taking into account structural breaks.

The non-linear and non-stationary nature of financial time series data poses significant challenges for standalone statistical and neural network methods. While predictive modeling in finance often focuses on volatility, there is a notable lack of research on predicting actual stock prices, particularly in the African market. This study addresses this gap by utilizing Airtel stock data from Yahoo Finance, spanning June 28, 2019, to May 8, 2024. The research employs the GARCH model to extract statistical properties, which are then combined with historical prices and fed into LSTM, GRU, and Transformer models leading to GARCH-LSTM, GARCH-GRU, GARCH-Transfomer hybrid models. These hybrid models are benchmarked against standalone LSTM, GRU and Transfomer models using RMSE, MAE, MAPE, and R-squared metrics. Results indicate that hybrid models, especially GARCH-LSTM, significantly outperform standalone models. This integration of GARCH with advanced AI models offers a more robust framework for stock price prediction, enhancing accuracy and reliability in forecasting future prices.