GARCH Research Articles

On an asymmetric functional-coefficient ARCH-M model

This paper proposes an asymmetric functional-coefficient autoregressive conditional heteroscedasticity in mean (ARCH-M) model, which allows for asymmetry in the volatility. The profile likelihood approach is applied to estimate the parametric and nonparametric components. Under some regularity assumptions, we derive asymptotic behavior of the proposed estimator. To avoid model misspecification, the Wald, quasi-likelihood ratio test statistic and generalized likelihood ratio test statistic are put forward to detect ARCH effect, asymmetric effect and goodness-of-fit, respectively. Moreover, their asymptotic distributions are established under both null and alternative hypotheses. Some Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed estimation methodology and testing procedure. Also, real data sets are analyzed to demonstrate the applications of the proposed model.

Downside risk in Dow Jones equity markets: hedging and portfolio management during COVID-19 pandemic and the Russia–Ukraine war

PurposeThis paper aims to examine the dynamic conditional correlation (DCC) and hedging ratios between Dow Jones markets and oil, gold and bitcoin. Using daily data, including the COVID-19 pandemic and the Russia–Ukraine war. We employ the DCC-generalized autoregressive conditional heteroskedasticity (GARCH) and asymmetric DCC (ADCC)-GARCH models.Design/methodology/approachDCC-GARCH and ADCC-GARCH models.FindingsThe most of DCCs among market pairs are positive during COVID-19 period, implying the existence of volatility spillovers (Contagion-effects). This implies the lack of additional economic gains of diversification. So, COVID-19 represents a systematic risk that resists diversification. However, during the Russia–Ukraine war the DCCs are negative for most pairs that include Oil and Gold, implying investors may benefit from portfolio-diversification. Our hedging analysis carries significant implications for investors seeking higher returns while hedging their Dow Jones portfolios: keeping their portfolios unhedged is better than hedging them. This is because Islamic stocks have the ability to mitigate risks.Originality/valueOur paper may make a valuable contribution to the existing literature by examining the hedging of financial assets, including both conventional and Islamic assets, during periods of stability and crisis, such as the COVID-19 pandemic and the Russia–Ukraine war.

Examining the dynamics of risk, performance, and volatility during COVID-19: Evidence from Moroccan stock market

This study delves into the repercussions of the COVID-19 pandemic on the Moroccan stock market, with a specific focus on the MASI index and sectoral indices. The examination en-compasses distinct pre-COVID and during-COVID periods, shedding light on the market’s evolution, marked by unique phases and fluctuations. Notably, the MASI index experienced a significant downturn in March 2020, indicative of the pandemic’s disruptive impact on investor behavior. Despite this setback, the market showcased remarkable resilience, staging a swift recovery and surpassing pre-crisis levels by the close of 2020. This rebound can be attributed to various factors, including historically low bond yields, the initiation of vaccination campaigns, and the resumption of dividend payouts by the banking sector. Our findings bring forth a nuanced understanding of performance and risk dynamics across individual sectors. Moreover, there is a noteworthy surge in correlations between sectoral returns during the COVID-19 period, limiting diversification options for investors and exposing them to heightened risks. The volatility patterns, analyzed using GARCH models, underscore the dynamic nature of the MASI index, exhibiting stability in the pre-pandemic phase and a transient disturbance during the initial pandemic shock. This study contributes to the existing body of literature on the global financial impact of COVID-19, providing valuable insights into the Moroccan context. The results emphasize the significance of comprehending sector-specific vulnerabilities and market dynamics for both investors and policymakers. In navigating the uncertainties of the post-pandemic era, these insights offer crucial perspectives for market participants to make informed decisions and adapt optimal strategies.

Research on Tail Risk Hedging in the Digital Asset Market

In recent years, the digital asset market has experienced rapid growth, but at the same time, its implicit tail risks have gradually raised concerns, especially amidst the global economic downturn caused by the pandemic. This paper aims to study tail risks and propose hedging strategies. Based on the GARCH and VaR models, this paper uses weekly return data from July 2017 to December 2021 for Bitcoin digital cryptocurrency and traditional non-digital asset market indices such as stocks, bonds, gold, and commodities. Utilizing EViews and Excel, the study explores tail risk measurement and portfolio diversification effects in the digital asset market. The main findings are as follows: (1) During the sample period, cryptocurrency returns exhibited significant volatility, with weak correlations with returns from traditional non-digital assets. Further analysis revealed strong hedging effects of digital assets against the bond market but weaker effects against the gold and stock markets, as well as commodity markets; (2) Cryptocurrency in traditional investment portfolios can enhance the risk-return ratio by adding it to the asset mix.

Electricity market price forecasting using ELM and Bootstrap analysis: A case study of the German and Finnish Day-Ahead markets

Electricity market liberalization and the absence of cost-efficient energy storage technologies have led to the transformation of state-owned electricity companies into complex electricity market entities, each having a different time horizon. Deregulation has intensified competition, giving rise to increased uncertainty caused by a multitude of interrelated exogenous factors, resulting in unexpected fluctuations in electricity prices. As a consequence, market participants encounter elevated risks and seek effective mitigation strategies. In this paper, the challenges described in the literature are addressed by studying price distribution histograms in the German and Finnish electricity markets. The objective is to identify normal price intervals that can serve as a foundation for an integrated Day-Ahead price forecasting methodology. A novel approach utilizing the Extreme Learning Machine in combination with Bootstrap intervals is proposed and applied to both markets. The findings demonstrate that Bootstrap intervals effectively capture normal prices, whereas extremely high prices typically align with the upper limits of Bootstrap intervals. Conversely, negative prices tend to fall outside the lower boundaries of the intervals. In order to assess the performance of the proposed methodology, a comparative analysis of its forecasting accuracy against the well-established Generalized AutoRegressive Conditional Heteroskedasticity and AutoRegressive Fractionally Integrated Moving Average models is conducted. In addition, both the computational efficiency and forecasting accuracy of the Extreme Learning Machine in comparison to the Artificial Neural Network are assessed. The results reveal the superior efficiency of the Extreme Learning Machine. The developed forecasting model could potentially assist market participants in making well-informed decisions and executing optimal bidding strategies in response to various scenarios before the Day-Ahead market closes. Notably, the proposed methodology transcends the limitations of fixed price thresholds and effectively addresses market nuances, including the occurrence of negative prices, thus offering a more comprehensive approach for electricity price forecasting.

Optimal hedging efficiency in global freight markets: Comparing FFAs and time charter strategies

The paper aims to mitigate financial risk in highly volatile shipping freight markets by employing a dynamic hedging model. The primary criterion for evaluating the effectiveness of various methods for estimating optimal hedge ratios through Forward Freight Agreements (FFAs) is the minimum variance hedging rule. Four different methods are utilized to estimate two types of hedge ratios. The first type, a static hedge ratio, is calculated using the OLS and ECM methods. The second type, a time-varying hedge ratio, is determined through a bivariate GARCH model and a Rolling Window OLS method. Additionally, the hedging effectiveness of the traditional method of hedging, time chartering, is compared to the more modern and sophisticated shipping derivatives methods using the coefficient of variation. Highlights Estimating optimal hedge ratios through Forward Freight Agreements (FFAs) with the minimum variance hedging rule Four different methods are utilized to estimate two types of hedge ratios for static and dynamic hedging Assess the hedging effectiveness of the different methods of hedge ration estimation Compare the hedging effectiveness of the traditional method of hedging, time chartering, to the more modern and sophisticated shipping derivatives methods using the coefficient of variation

Trade Agreements and Financial Market Integration in Latin America and the US

The primary objective of this study is to examine the extent of financial integration between Latin American and US financial markets, particularly in light of recent efforts to foster integration through trade agreements. Spanning from 1 January 1990 to 31 December 2019, the sample focuses on major market indices and key sectors. Financial integration is quantified using a DCC multivariate GARCH model, incorporating a smooth transition model, structural breaks, and regression-based approaches. Results indicate increased comovement with the US for main market indices in Argentina, Chile, Colombia, Mexico, and Peru, while Brazil shows a decrease. Similar trends are observed in sectoral analyses. This study also reveals heightened correlation post-trade agreements. Structural break analysis highlights significant shifts in dynamic correlations for countries with US free trade agreements. These findings support the argument of increased financial integration, bearing significance for portfolio diversification and international policy formulation.

Predicting tail risks by a Markov switching MGARCH model with varying copula regimes

AbstractTo improve the dynamic assessment of risks of speculative assets, we apply a Markov switching MGARCH approach to portfolio risk forecasting. More specifically, we take advantage of the flexible Markov switching copula multivariate GARCH (MS‐C‐MGARCH) model of Fülle and Herwartz (2022). As an empirical illustration, we take the perspective of a risk‐averse agent and employ the suggested model for assessments of future risks of portfolios composed of a high‐yield equity index (S&P 500) and two safe‐haven investment instruments (i.e., Gold and US Treasury Bond Futures). We follow recent suggestions to employ the expected shortfall as a prime assessment of tail risks. To accurately evaluate the merits of the new model, we back‐test the risk forecasting for daily returns over 10 years for heterogeneous market environments including, for example, the COVID‐19 pandemic. We find that the MS‐C‐MGARCH model outperforms benchmark volatility models (MGARCH, C‐MGARCH) in predicting both value‐at‐risk and expected shortfall. The superiority of the MS‐C‐MGARCH model becomes stronger, when the share of comparably risky assets in the portfolio is relatively large.

Volatility forecasting and assessing risk of financial markets using multi-transformer neural network based architecture

This research introduces a more reliable model for predicting market volatility. The model incorporates Transformer and Multi-transformer layers with the GARCH and LSTM models and compares their performance to classic GARCH-type models. Euro-US Dollar FX Spot Rate (EURO-USD), Australian-US Dollar FX Spot Rate (AUD-USD), S&P 500 Index, FTSE 100 Index, Reliance Industries Ltd., and Samsung Electronics Co Ltd. are analyzed. The timeframe examined is January 2005 to December 2021, with training from 2005 to 2016 and testing from 2017 to 2021. Empirical evidence suggests that hybrid Neural-network models, notably Transformer-based models, outperform individual transformers, deep learning, neural networks, and traditional GARCH-type models, even in unpredictable conditions like the COVID-19 pandemic. Within the hybrid Neural-network models, MT-GARCH and MTL-GARCH showed lower validation error (RMSE) than the other models, showing that the bagging mechanism added to the attention mechanism of the Multi-Transformer architecture helped to lower the error in the variance in the noisy data of the daily returns of the assets, reducing the RMSE of the hybrid multi-Transformer models. In addition, three to four of the five hybrid neural-network models showed appropriate risk estimates for the entire test period, as observed from the Christoffersen test. Moreover, the lengthy sample period helps test whether hybrid models perform better than classic GARCH-type models in volatile conditions like the COVID-19 pandemic.

The Impacts of Global Factors on Islamic Stock Market Returns: Evidence From Islamic Countries

This study investigates the impact of five (5) global factors, namely in this study such as global economic policy uncertainty, geopolitical risks, oil prices, volatility index, and world uncertainty index, on six (6) Islamic stock markets in Australia, Bahrain, Indonesia, Kuwait, Malaysia, and Oman. The monthly data for 13 years from 2009:M3 to 2023:M5 within a time-frequency framework. We used the GARCH model to investigate the impacts of global factors on selected Islamic stock market returns, and the EGARCH model was used to check the robustness of the results. The results provide a few interesting insights. Firstly, it is important to note that GEPU, GPR, OIL, and VIX uncertainty typically exert a significant influence on the majority of Islamic stock returns. Secondly, WUI demonstrates an important relationship in Australia, Bahrain, and Oman only following the outbreak of the COVID-19 pandemic. These results should assist investors in re-evaluating their portfolio to fully maximize the potential of these Islamic stock markets. Policymakers could use these results to design policies to reduce the global factors as well as to investigate the impacts of externally generated uncertainties.

A Study on the Nature of Complexity in the Spanish Electricity Market Using a Comprehensive Methodological Framework

The existence of chaos is particularly relevant, as the identification of a chaotic behavior in a time series could lead to reliable short-term forecasting. This paper evaluates the existence of nonlinearity and chaos in the underlying process of the spot prices of the Spanish electricity market. To this end, we used daily data spanning from 1 January 2013, to 31 March 2021 and we applied a comprehensive framework that encompassed a wide range of techniques. Nonlinearity was analyzed using the BDS method, while the existence of a chaotic structure was studied through Lyapunov exponents, recurrence plots, and quantitative recurrence analysis. While nonlinearity was detected in the underlying process, conclusive evidence supporting chaos was not found. In addition, the generalized autoregressive conditional heteroscedastic (GARCH) model accounts for part of the nonlinear structure that is unveiled in the electricity market. These findings hold substantial value for electricity market forecasters, traders, producers, and market regulators.

Monetary Policy on Exchange Rate Volatility in Nigeria: Evidence from BARDL/ARCH and Garch Modellings

While the impact of monetary policy on the exchange rate has been explored in the literature, the volatility of the exchange rate remains an important issue of concern. This study examines the impact of monetary policy on exchange rate volatility in Nigeria. The study uses annual time series data covering 1987 until 2023 which was analysed using Autoregressive Conditional Heteroscedasticity (ARCH), bootstrap bound test for cointegration and Granger causality test within the vector error correction model. The empirical finding of the ARCH reveals the presence of conditional volatility of the exchange rate. Moreover, findings from the bootstrap bound test establish a long-run relation among the variables. The study further found that the volatility of the exchange rate is accounted for by the changes in money supply and previous fluctuation of the exchange rate. The causality test indicates the existence of causality from exchange rate volatility to money supply, interest rate, saving and population in both in short and long run. The study concludes that the volatility of the exchange rate is driven by the variability of money supply, interest rate and savings. Therefore, controlling the shocks emanating from previous exchange rate volatility and money supply is key to addressing the exchange rate fluctuation in Nigeria. The study recommends a policy mix of utilizing key fiscal and monetary policy tools that could enable Nigeria to achieve exchange rate stability.

Time-varying Connectedness Between ESG Stocks and BRVM Traditional Stocks

Periods of crisis prompt investors to look out for means of making returns even in uncertain market conditions. Investors are using stocks selected on an environmental, social, and governance (ESG) basis to mitigate the unavoidable risks of investing in assets during these times of pandemic and war. In an integrated global financial system, we sought to explore the connectedness, if any, between the returns on the Bourse Régionale des Valeurs Mobilières (BRVM) and ESG-based stocks. Using a time-varying parameter vector autoregression (TVP-VAR) to analyze daily returns from 12 March 2013 to 4 April 2022, we find categorically that ESG-based stocks and BRVM stocks are connected, with ESG-based stocks dominating the network connectedness. Furthermore, using dynamic connectedness correlations from dynamic conditional correlation generalized autoregressive conditional heteroscedasticity (DCC-GARCH), we show that ESG stocks could be used as a safe haven or weak hedge for BRVM stocks in times of crisis. We test for the robustness of our findings using quantile causality. The causality test further shows that ESG-based stocks cause movements in BRVM stocks mostly at the lower quantiles—enhancing the findings of dominancy from the TVP-VAR estimates and offer diversification and safe haven benefits from the DCC-GARCH in extreme conditions. The implication of these findings for investors is that they could benefit from using ESG-based stocks in their portfolios, particularly in times of crisis. JEL Codes: G01, G11

Dynamic Analysis of a Double-Cable-Stayed Shallow Arch Model Under Multi-Frequency Excitation by IHB Method

To reveal the dynamic properties of cable-stayed bridges under complex external excitations, a double-cable-stayed shallow arch model induced by multi-frequency harmonic excitations is established. The cable and shallow arch exhibit primary or subharmonic resonances by sweeping excitations simultaneously and asynchronously. Galerkin method, one/two time scales Incremental Harmonic Balance (IHB) method, and Runge–Kutta (RK) method are applied to explore the nonlinear dynamic responses. Research results demonstrate that both the cables and shallow arch present soft and hard spring properties, despite the very weak hard spring of the shallow arch; one-way dynamic interaction among the cables and the shallow arch is discovered when sweeping excitations asynchronously.

Forecasting the volatility of crude oil basis: Univariate models versus multivariate models

The studies on investigating and forecasting crude oil volatility primarily focus on oil price volatility. This research aims to forecast the volatility of the oil futures basis using generalized auto regressive conditional heteroskedasticity (GARCH) and its extended models. Specifically, this study compares the forecasting performance of nine econometric models, including two univariate and seven multivariate models. The empirical results show that simple univariate models outperform the multivariate models in forecasting basis volatility, as indicated by the model confidence set (MCS). Moreover, from an economic perspective, the empirical results also demonstrate that the univariate models generate higher Sharpe ratios than the multivariate ones, consistent with the statistical evaluation results on forecasting accuracy.

Sovereign Credit Default Swap Market Volatility in BRICS Countries Before and During the COVID-19 Pandemic

SCDS (Sovereign Credit Default Swaps) are becoming more widely used as a country risk indicator after 2008 and stand out for providing real-time information rather than periodic reporting. The COVID-19 pandemic has led to economic disruptions and a decline in international trade. Understanding how the Pandemic affects SCDS return volatility in emerging economies like BRICS forms the motivation for our research. With this study, we aim to determine the impact of the COVID-19 Pandemic on SCDS return volatility in Brazil, Russia, India, China and South Africa, known as the BRICS countries. We used the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model to analyze the data, which consisted of the daily closing price data for SCDS. The date of the first COVID-19 case in each country has been taken as the beginning of the COVID-19 Pandemic in each country. The results of the estimated GARCH models show that the volatility processes of the SCDS return series differ between periods. EGARCH model results indicate that shocks created by news in these countries during the Pandemic have a small and persistent effect on Brazil and Russia's SCDS return volatility, while they have a large and enduring effect on China and South Africa's SCDS return volatility. The findings will guide policymakers and portfolio managers in determining risk management models.

Vulnerability of a developing stock market to openness: One-way return and volatility transmissions

Drawing from two independent literature sources on vulnerability and stock price volatility, we show that the high magnitude and persistence of stock return volatility evident in the Nigerian Exchange Group (NGX) are, at least in part, indications of vulnerability to openness, which paves the way for the transmission of external shocks. Using a uniquely modified set of bivariate asymmetric GARCH models, we investigate one-way return and volatility transmissions from the international Brent oil market, natural gas markets, carbon markets, and naira-dollar exchange market to the NGX. Firstly, we document direct and asymmetric return and volatility transmissions from the Brent oil market to the NGX, denoting the fragile sensitivity of the NGX to international oil price turbulence. Secondly, we find a direct volatility transmission from natural gas markets to the NGX, implying an increasing reliance on natural gas exports by the Nigerian government. Thirdly, we document an inverse volatility transmission from carbon markets to the NGX, indicating Nigeria's negative reaction, as a major oil and gas producer, to increasing global sustainable production activities. Fourthly, the insignificant effect of the naira-dollar official exchange rate on volatility in the NGX demonstrates the spurious impression that Nigeria's exertion of control over the exchange rate is shielding the economy. In sum, our results confirm that the openness of the NGX makes it vulnerable to external shock transmissions from related external markets subsisting outside Nigeria. Our results are robust to an alternative estimation procedure that employs a different measure of price volatility from the three external markets.

Diversification, hedging, and safe-haven characteristics of cryptocurrencies: A structural change approach

This study investigates the influence of structural change on the diversification, hedging, and safe-haven characteristics of Bitcoin and Ethereum against various financial assets such as gold, the US Dollar Index, stock indices, oil, and commodity indices from August 7, 2015, to August 15, 2022, using the DCC–ARMA–GARCH models with the CUSUM test. Our results indicate that cryptocurrencies have the same characteristics vis-à-vis financial markets during the entire sample period and periods tied to the date of major international events (COVID-19 and the early-2022 Russia–Ukraine War). However, we find that cryptocurrencies play different roles against specific asset markets in different periods separated by structural change models. Our findings suggest that incorporating structural changes into a model accounts for higher volatility and may better describe the real-world capabilities of cryptocurrencies against financial assets.

Biomechanical Effects of Different Auxiliary–Aligner Designs on the Rotation of an Upper Canine: A Finite Element Analysis of a Specific Patient

Aim: The objective of this research has been to apply a specific simulation to a patient to assess the biomechanical consequences of rotating an upper canine tooth through different attachment–aligner configurations and to predict the most efficient design using a three-dimensional finite element model of a full maxillary arch of a specific patient. Materials and methods: This was obtained by combining Cone-Beam Computed Tomography (CBCT) with the aim of reconstructing tooth roots and bone tissues, and Surface Structured-Light Scanning for creating digital tooth crown models from the patient’s impressions. This model was imported into the finite element solver (Ansys® 17). Three different attachment–aligner combinations were created through the exploitation of computer-aided design (CAD) procedures, i.e., without attachments, with a couple of attachments and with an attachment and a pressure point. For each simulation, the resulting force–moment (MF) system applied by the aligner to the target tooth, as well as the tooth displacement and rotation, was computed using a workstation based on Intel Xeon CPU E3-1245 v3@3.40 GHz and 16 GB RAM. Simulations reported that by adding the pressure point and the attachment to the standard aligner the amount of Moment z (Mz) delivered to the tooth increased almost two times. Results and conclusions: The maximum tooth displacement (0.85 mm) was obtained with the attachment and pressure point aligner, while the lowest (0.058 mm) was obtained with use of a couple of attachments. Both the attachment and the pressure point have the potential to enhance the appliance’s effectiveness. Particularly, the pressure point showed a higher influence on the load absolute value. The method applied in the present study should be used to retrieve the best design configuration for each patient and specific tooth movement.

Day-of-the-Week and Month-of-the-Year Effects in the Cryptocurrency Market

This study examines the day-of-the-week (DoW) and month-of-the-year (MoY) effects in the cryptocurrency market, with a focus on Bitcoin (BTC) and Ethereum (ETH). Due to the absence of a specific closing time in the cryptocurrency market, the closing time of the daily data is taken as 23:59 UTC. Initially, an appropriate volatility model for the cryptocurrency market is established using the GARCH, EGARCH, and TGARCH models. The most appropriate model for BTC is ARMA(1,0)-EGARCH(1,1) and ARMA(1,0)-GARCH(1,1) for ETH. The results of the analysis indicate a leverage effect in the cryptocurrency market, where negative shocks cause a more significant increase in volatility than positive shocks. Based on this volatility structure, the DoW and MoY are analyzed. For BTC, returns on other days are lower compared to Mondays. However, for ETH, returns on Thursdays are lower than those on Mondays. In terms of volatility, both BTC and ETH show that the highest volatility occurs on Mondays. For the MoY effect, neither BTC nor ETH don’t exhibit a significant effect in the mean equation. Nevertheless, the variance equation indicates that January has higher volatility compared to other months, indicating the presence of a MoY effect in terms of volatility.