Search Results (24)

In numerous domains of finance and economics, modelling and predicting stock market volatility is essential. Predicting stock market volatility is widely used in the management of portfolios, analysis of risk, and determination of option prices. This study is about volatility modelling of the daily Johannesburg Stock Exchange All Share Index (JSE ALSI) stock price data between 1 January 2014 and 29 December 2023. The modelling process incorporated daily log returns derived from the JSE ALSI. The following volatility models were presented for the period: sGARCH(1, 1) and fGARCH(1, 1). The models for volatility were fitted using five unique error distribution assumptions, including Student’s t, its skewed version, the generalized error and skewed generalized error distributions, and the generalized hyperbolic distribution. Based on information criteria such as Akaike, Bayesian, and Hannan–Quinn, the ARMA(0, 0)-fGARCH(1, 1) model with a skewed generalized error distribution emerged as the best fit. The chosen model revealed that the JSE ALSI prices are highly persistent with the leverage effect. JSE ALSI price volatility was notably influenced during the COVID-19 pandemic. The forecast over the next 10 days shows a rise in volatility. A comparative study was then carried out with the JSE Top 40 and the S&P500 indices. Comparison of the FTSE/JSE Top 40, S&P 500, and JSE ALLSI return indices over the COVID-19 pandemic indicated higher initial volatility in the FTSE/JSE Top 40 and S&P 500, with the JSE ALLSI following a similar trend later. The S&P 500 showed long-term reliability and high rolling returns in spite of short-run volatility, the FTSE/JSE Top 40 showed more pre-pandemic risk and volatility but reduced levels of rolling volatility after the pandemic, similar in magnitude for each index with low correlations among them. These results provide important insights for risk managers and investors navigating the South African equity market. Full article

The purpose of this study is to conduct an empirical comparative study of volatility models for three of the most popular cryptocurrencies. We study the volatility of the following cryptocurrencies: Bitcoin, Ethereum, and Litecoin. We consider the GARCH-type, boosting-family-tree-based ensemble learning, and ANFIS volatility models for these financial crypto-assets, which some have claimed capture stylized facts about cryptocurrency volatility well. We conduct comparative studies on in-sample and out-of-sample empirical analyses. The results show that tree-based ensemble learning delivers better forecast accuracy. Nevertheless, the performance of some GARCH-type volatility models is relatively close to that of the best model on both training and evaluation samples. Full article

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov’s principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for “uncertain” drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented. Full article

This study investigates calendar anomalies and their impact on returns and volatility patterns in the cryptocurrency market, focusing on day-of-the-week effects before and during the COVID-19 pandemic. Using advanced statistical models from the GARCH family, we analyze the returns of Binance USD, Bitcoin, Binance Coin, Cardano, Dogecoin, Ethereum, Solana, Tether, USD Coin, and Ripple. Our findings reveal significant shifts in volatility dynamics and day-of-the-week effects on returns, challenging the notion of market efficiency. Notably, Bitcoin and Solana began exhibiting day-of-the-week effects during the pandemic, whereas Cardano and Dogecoin did not. During the pandemic, Binance USD, Ethereum, Tether, USD Coin, and Ripple showed multiple days with significant day-of-the-week effects. Notably, positive returns were generally observed on Sundays, whereas a shift to negative returns on Mondays was evident during the COVID-19 period. These patterns suggest that exploitable anomalies persist despite the market’s continuous operation and increasing maturity. The presence of a long-term memory in volatility highlights the need for robust trading strategies. Our research provides valuable insights for investors, traders, regulators, and policymakers, aiding in the development of effective trading strategies, risk management practices, and regulatory policies in the evolving cryptocurrency market. Full article

This paper investigates how the introduction of foreign exchange futures has an impact on spot volatility and considers the contemporaneous and dynamic relationship between spot volatility and foreign exchange futures trading activity, including trading volume and open interest in the Thailand Futures Exchange context, with the examples of the EUR/USD futures and USD/JPY futures. The results of the EGARCH (1,1) model show that the introduction of foreign exchange futures decreases spot volatility. It also increases the rate at which new information is impounded into spot prices but decreases the persistency of volatility shocks. A positive effect of unexpected trading volume and a negative effect of unexpected open interest on contemporaneous spot volatility are in line with the VAR(1) model results of the dynamic relationship between spot volatility and foreign exchange futures trading activity. With the impact on spot volatility caused by unexpected open interest rate being stronger than by unexpected trading volume, foreign exchange futures trading stabilizes spot volatility. Full article

As a type of financial derivative, the price fluctuation of futures is influenced by a multitude of factors, including macroeconomic conditions, policy changes, and market sentiment. The interaction of these factors makes the future trend become complex and difficult to predict. However, for investors, the ability to accurately predict the future trend of stock index futures price is directly related to the correctness of investment decisions and investment returns. Therefore, predicting the stock index futures market remains a leading and critical issue in the field of finance. To improve the accuracy of predicting stock index futures price, this paper introduces an innovative forecasting method by combining the strengths of Long Short-Term Memory (LSTM) networks and various Generalized Autoregressive Conditional Heteroskedasticity (GARCH)-family models namely, MULTI-GARCH-LSTM. This integrated approach is specifically designed to tackle the challenges posed by the nonstationary and nonlinear characteristics of stock index futures price series. This synergy not only enhances the model’s ability to capture a wide range of market behaviors but also significantly improves the precision of future price predictions, catering to the intricate nature of financial time series data. Initially, we extract insights into the volatility characteristics, such as the aggregation of volatility in futures closing prices, by formulating a model from the GARCH family. Subsequently, the LSTM model decodes the complex nonlinear relationships inherent in the futures price series and incorporates assimilated volatility characteristics to predict future prices. The efficacy of this model is validated by applying it to an authentic dataset of gold futures. The empirical findings demonstrate that the performance of our proposed MULTI-GARCH-LSTM hybrid model consistently surpasses that of the individual models, thereby confirming the model’s effectiveness and superior predictive capability. Full article

Carbon trading risk management and policy making require accurate forecasting of carbon trading prices. Based on the sample of China’s carbon emission trading pilot market, this paper firstly uses the Augmented Dickey–Fuller test and Autoregressive conditional heteroscedasticity model to test the stationarity and autocorrelation of carbon trading price returns, uses the Generalized Autoregressive Conditional Heteroscedasticity family model to analyze the persistence, risk and asymmetry of carbon trading price return fluctuations, and then proposes a hybrid prediction model neural network (generalized autoregressive conditional heteroscedasticity–long short-term memory network) due to the shortcomings of GARCH models in carbon price fluctuation analysis and prediction. The model is used to predict the carbon trading price. The results show that the carbon trading pilots have different degrees of volatility aggregation characteristics and the volatility persistence is long, among which only the Shanghai and Beijing carbon trading markets have risk premiums. The other pilot returns have no correlation with risks, and the fluctuations of carbon trading prices and returns are asymmetrical. The prediction results of different models show that the root mean square error (RMSE) of Hubei, Shenzhen and Shanghai carbon trading pilots based on the GARCH-LSTM model is significantly lower than that of the single GARCH model, and the RMSE values are reduced by 0.0006, 0.2993 and 0.0151, respectively. The RMSE in the three pilot markets improved by 0.0007, 0.3011 and 0.0157, respectively, compared to the standalone LSTM model. At the same time, compared with the single model, the GARCH-LSTM model significantly increased the R^2 value in Hubei (0.2000), Shenzhen (0.7607), Shanghai (0.0542) and Beijing (0.0595). Therefore, compared with other models, the GARCH-LSTM model can significantly improve the prediction accuracy of carbon price and provide a new idea for scientifically predicting the fluctuation of financial time series such as carbon price. Full article

Due to environmental concerns, electric vehicles (EVs) are gaining traction over fossil fuel-based vehicles. For electronic devices, including vehicles, copper is the key material used for building. This situation draws attention to the impact of copper prices, crude oil prices, and exchange rates on the economic viability of using EVs over fossil fuels. We use the volatility spillover effect (VSE) to determine the financial viability of these two types of vehicles in the context of environmental issues. Daily data on copper prices, crude oil, exchange rate, and the BSE100 ESG (“Bombay Stock Exchange 100 Environmental, Social and Governance”) index are taken from 1 November 2017 to 20 September 2022. Two popular multivariate GARCH (“Multivariate Generalized Autoregressive Conditional Heteroscedasticity”) family models, i.e., the BEKK (“Baba–Engle–Kraft–Kroner”)-GARCH (BG) and DCC (“Dynamic Conditional Correlation”)-GARCH (DG) models, are utilized to find volatility connections between these variables. These are appropriate GARCH models to observe the volatility dependence of one market on another market. It is found that there exist volatility effects of copper and exchange rate on the S&P BSE100 ESG Equity Index Price, which we will refer to here as ESG. However, crude oil is found to be insignificant for ESG. The novelty of this study is in the use of volatility spillover to determine economic viability. The volatility effects of copper prices are positive for ESG in the short run and negative for long-term volatility. The exchange rate has a positive volatility effect on ESG in the long run. Surprisingly, we find that EVs are technologically better than fossil fuel-based vehicles as a possible sustainable energy source. We observe studies that have raised similar concerns about EVs’ lack of business sense compared to fossil fuels. However, using VSE to explore financial viability offers a fresh perspective. Based on the findings of the current study, it is recommended that policymakers and researchers revisit their support for EVs as an alternate and sustainable source of energy. Full article

Across the globe, COVID-19 has disrupted the financial markets, making them more volatile. Thus, this paper examines the market volatility and asymmetric behavior of Bitcoin, EUR, S&P 500 index, Gold, Crude Oil, and Sugar during the COVID-19 pandemic. We applied the GARCH (1, 1), GJR-GARCH (1, 1), and EGARCH (1, 1) econometric models on the daily time series returns data ranging from 27 November 2018 to 15 June 2021. The empirical findings show a high level of volatility persistence in all the financial markets during the COVID-19 pandemic. Moreover, the Crude Oil and S&P 500 index shows significant positive asymmetric behavior during the pandemic. Apart from this, the results also reveal that EGARCH is the most appropriate model to capture the volatilities of the financial markets before the COVID-19 pandemic, whereas during the COVID-19 period and for the whole period, each GARCH family evenly models the volatile behavior of the six financial markets. This study provides financial investors and policymakers with useful insight into adopting effective strategies for constructing portfolios during crises in the future. Full article

The frequent and sharp fluctuations in garlic prices seriously affect the sustainable development of the garlic industry. Accurate prediction of garlic prices can facilitate correct evaluation and scientific decision making by garlic practitioners, thereby avoiding market risks and promoting the healthy development of the garlic industry. To improve the prediction accuracy of garlic prices, this paper proposes a garlic-price-prediction method based on a combination of long short-term memory (LSTM) and multiple generalized autoregressive conditional heteroskedasticity (GARCH)-family models for the nonstationary and nonlinear characteristics of garlic-price series. Firstly, we obtain volatility characteristic information such as the volatility aggregation of garlic-price series by constructing GARCH-family models. Then, we leverage the LSTM model to learn the complex nonlinear relationships between the garlic-price series and the volatility characteristic information of the series, and predict the garlic price. We applied the proposed model to a real-world garlic dataset. The experimental results show that the prediction performance of the combined LSTM and GARCH-family model containing volatility characteristic information of garlic price is generally better than those of the separate models. The combined LSTM model incorporating GARCH and PGARCH models (LSTM-GP) had the best performance in predicting garlic price in terms of evaluation indexes, such as mean absolute error, root mean-square error, and mean absolute percentage error. The combined model of LSTM-GARCH provides the best results in garlic price prediction and can provide support for garlic price prediction. Full article

Cryptocurrencies have gained a lot of attraction across the globe. Most observers of the cryptocurrency market will agree that crypto volatility is in a different league altogether. There has been a growing need to understand the nature of volatility in cryptocurrency. This paper analyzes the performance of four mostly traded, different cryptocurrencies in terms of their risk and return. The relationship between the return and returns volatility among different currencies has been examined considering the daily closing prices from 1 January 2017 to 30 June 2022, using the family of the GARCH model. The study has explored the spillover and asymmetric effect of volatility by using the DCC GARCH model and EGARCH model, respectively. The causal behavior among different cryptocurrencies has also been examined using Granger causality. There has been a strong spillover effect among different cryptocurrencies, Bitcoin and Ether, which are the top two cryptocurrencies with the highest market capitalization which have exhibited an asymmetric impact in their volatility as compared to the other two currencies, which are Litecoin and XRP. Full article

Traffic volatility modeling has been highly valued in recent years because of its advantages in describing the uncertainty of traffic flow during the short-term forecasting process. A few generalized autoregressive conditional heteroscedastic (GARCH) models have been developed to capture and hence forecast the volatility of traffic flow. Although these models have been confirmed to be capable of producing more reliable forecasts than traditional point forecasting models, the more or less imposed restrictions on parameter estimations may make the asymmetric property of traffic volatility be not or insufficiently considered. Furthermore, the performance of the models has not been fully evaluated and compared in the traffic forecasting context, rendering the choice of the models dilemmatic for traffic volatility modeling. In this study, an omnibus traffic volatility forecasting framework is proposed, where various traffic volatility models with symmetric and asymmetric properties can be developed in a unifying way by fixing or flexibly estimating three key parameters, namely the Box-Cox transformation coefficient $\lambda$, the shift factor $b$, and the rotation factor $c$. Extensive traffic speed datasets collected from urban roads of Kunshan city, China, and from freeway segments of the San Diego Region, USA, were used to evaluate the proposed framework and develop traffic volatility forecasting models in a number of case studies. The models include the standard GARCH, the threshold GARCH (TGARCH), the nonlinear ARCH (NGARCH), the nonlinear-asymmetric GARCH (NAGARCH), the Glosten–Jagannathan–Runkle GARCH (GJR-GARCH), and the family GARCH (FGARCH). The mean forecasting performance of the models was measured with mean absolute error (MAE) and mean absolute percentage error (MAPE), while the volatility forecasting performance of the models was measured with volatility mean absolute error (VMAE), directional accuracy (DA), kickoff percentage (KP), and average confidence length (ACL). Experimental results demonstrate the effectiveness and flexibility of the proposed framework and provide insights into how to develop and select proper traffic volatility forecasting models in different situations. Full article

Tourism forecasting has garnered considerable interest. However, integrating tourism forecasting with volatility is significantly less typical. This study investigates the performance of both the single models and their combinations for forecasting the volatility of tourism demand. The seasonal autoregressive integrated moving average (SARIMA) model is used to construct the mean equation, and three single models, namely the generalized autoregressive conditional heteroscedasticity (GARCH) family models, the error-trend-seasonal exponential smoothing (ETS-ES) model, and the innovative smooth transition exponential smoothing (STES) model, are employed to estimate the volatility of monthly tourist arrivals into Malaysia. This study also assesses the accuracy of forecasts using simple average (SA), minimum variance (MV), and novel smooth transition (ST). STES performs the best of the single models for forecasting the out-of-sample of tourism demand volatility, followed closely by ETS-ES. In contrast, the ST combining method surpasses SA and MV. Interestingly, forecast combining methods do not always outperform the best single model, but they consistently outperform the worst single model. The MCS and DM tests confirm the aforementioned findings. This article merits consideration for future forecasting research on tourism demand volatility. Full article

Over the past years, cryptocurrencies have drawn substantial attention from the media while attracting many investors. Since then, cryptocurrency prices have experienced high fluctuations. In this paper, we forecast the high-frequency 1 min volatility of four widely traded cryptocurrencies, i.e., Bitcoin, Ethereum, Litecoin, and Ripple, by modeling volatility to select the best model. We propose various generalized autoregressive conditional heteroscedasticity (GARCH) family models, including an sGARCH(1,1), GJR-GARCH(1,1), TGARCH(1,1), EGARCH(1,1), which we compare to a multivariate DCC-GARCH(1,1) model to forecast the intraday price volatility. We evaluate the results under the MSE and MAE loss functions. Statistical analyses demonstrate that the univariate GJR-GARCH model (1,1) shows a superior predictive accuracy at all horizons, followed closely by the TGARCH(1,1), which are the best models for modeling the volatility process on out-of-sample data and have more accurately indicated the asymmetric incidence of shocks in the cryptocurrency market. The study determines evidence of bidirectional shock transmission effects between the cryptocurrency pairs. Hence, the multivariate DCC-GARCH model can identify the cryptocurrency market’s cross-market volatility shocks and volatility transmissions. In addition, we introduce a comparison of the models using the improvement rate (IR) metric for comparing models. As a result, we compare the different forecasting models to the chosen benchmarking model to confirm the improvement trends for the model’s predictions. Full article

In this study, we examine the effect of introducing SSE 50ETF index options trading on stock market volatility using a panel data evaluation approach. Based on the cross-sectional dependence among international stock indices and macroeconomic indicators, we estimate the counterfactual volatility of the SSE 50 index and find that the introduction of index options reduces stock market volatility significantly in the long term. The primary findings are robust to alternative econometric models, including principal component analysis, GARCH-family model, and LASSO regression. The results of this paper suggest that the introduction of SSE index options provides investors with risk management tools and improves price discovery in the stock market. Full article