Symmetric GARCH Research Articles

Value-at-risk modeling of naira exchange rates

The naira exchange rate has experienced extreme volatility, and the use of derivatives to control interest rates and currency risks has grown quickly. These developments have made risk management research necessary. To this effect, this paper investigated the optimal volatility model that offers the best VaR forecasts and minimizes expected loss in the Naira exchange rate. The data was collected from FX time and consisted of the Euro to Naira exchange and the daily closing rate of the US dollar to Naira exchange rate from 24/10/2016 to 15/06/2018. These data were estimated using different symmetric and asymmetric GARCH models. The finding shows that there is less volatility in the USD to Naira exchange rate compared to the Euro to Naira exchange rate. The study shows that SPLINE- GJR under skewed student t distribution is the optimal model for the Euro to Naira exchange rate while GARCH is the optimal model for the US dollar to Naira exchange rate. This study suggests that model risk assessments be given careful consideration by regulators, banks, and other stakeholders and integrated into the process of operational and regulatory design.

ESG performance and corporate volatility: an empirical exploration in an emerging economy

PurposeThis study aims to investigate into the dynamic connection between ESG scores and the volatility term structure for Indian companies listed BSE. The study divides the BSE-100 listed companies into two panels based on their median ESG scores in 2022, creating high and low ESG scoring groups to capture volatility structure.Design/methodology/approachThe study employs time-varying symmetric and asymmetric GARCH models and followed by continuous Wavelet to capture volatility structure and explore comparative resilience behavior.FindingsThe study found similar volatility patterns regardless of ESG scores, nudging doubt on the direct impact of ESG on volatility. Additionally, both high- and low-ESG-scored companies displayed high vulnerabilities during the pandemic, raising questions about the effectiveness of ESG frameworks in capturing risks. Finally, by examining the resilience behavior of ESG-scored companies during the pandemic, our study contributes to the evolving understanding of the intersection between ESG performance and crisis response.Practical implicationsThe study carries vital implications for investors and policymakers. It highlights the urgent need to strengthen the ESG framework and scores to shield investors from short- and long-term volatilities and economic vulnerabilities.Originality/valueTo the best of the authors’ knowledge, this is the first study investigating the Indian market by examining the volatility structure and resilience behavior of high- and low-ESG-scored companies during the pandemic.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/IJSE-02-2024-0113

Quantifying the Impact of Risk on Market Volatility and Price: Evidence from the Wholesale Electricity Market in Portugal

This research aims to identify suitable procedures for determining the size of risks to predict the tendency of electricity prices to return to their historical average or mean over time. The goal is to quantify the sensitivity of electricity prices to different types of shocks to mitigate price volatility risks that affect Portugal’s energy market. Hourly data from the beginning of January 2016 to December 2021 were used for the analysis. The symmetric and asymmetric GARCH model volatility, as a function of past information, help to eliminate excessive peaks in data fluctuations. The asymmetric model includes additional parameters to separately obtain the impact of positive and negative shocks on volatility. The MSGARCH model is estimated to be in two states, allowing for transitions between low- and high-volatility states. This approach effectively represents the significant impact of shocks in a high-volatility state, indicating an acknowledgment of the lasting effects of extreme events on financial markets. Furthermore, the MSGARCH model is designed to obtain the persistence of shocks during periods of elevated volatility. Accurate price forecasting aids power producers in anticipating potential price trends and allows them to adjust their operations by considering the overall stability and efficiency of the electricity market.

VOLATILITY ANALYSIS OF CRUDE OIL PRICES IN NIGERIA

This study investigates the symmetric and asymmetric characteristics as well as the persistence of shocks in the Nigerian crude oil returns, utilizing monthly and daily crude oil prices spanning from January 2006 to September 2022 and November 3, 2009, to November 4, 2022, respectively. Descriptive statistics, normality measures, time plots, and the Dickey-Fuller Generalized Least Squares unit root test were employed to analyze the series properties. Symmetric ARMA (1,1)-GARCH (2,1) and asymmetric ARMA (1,1)-TARCH (2,1) models for monthly and daily returns, with varying innovation densities, were utilized, alongside symmetric GARCH (1,1) and asymmetric TARCH (1,1) models. Model selection criteria including AIC, SIC, HQC, and log likelihood guided the order and error distribution selection. Results revealed non-normal distributions for both monthly and daily prices and returns, non-stationarity in prices, and weak stationarity in log returns with ARCH effects detected in both returns. Symmetric models exhibited volatility clustering, high shocks persistence, mean-reverting behaviour, and predictability in both returns. Asymmetric models identified asymmetry with leverage effects in both returns, indicating that negative shocks induce greater volatility than positive shocks of the same magnitude. Mean reversion and volatility half-life findings suggested that crude oil prices tend to revert to their long-run averages. The study recommended promoting market information flow and aggressive trading to enhance market depth and mitigate the volatile nature of the Nigerian crude oil market.

Modelling Inflation Rate Uncertainty in India: An Empirical Study

In recent years, the concept of volatility has gained much importance in macroeconomic variables like stock market indices, exchange rates and price indices. In this study, inflation indicators like the Consumer Price Index Combined (CPI-C) and Wholesale Price Index? all commodities (WPI-AC) starting in 2014:01 and ending in 2023:04 in India are used to measure the inflation uncertainty. To show volatility both symmetric and asymmetric models which are GARCH type are employed. So, that an appropriate forecasting model could be projected. For CPI an asymmetric GARCH model is found appropriate while for WPI a symmetric GARCH model was shown appropriate in the analysis. The volatility of CPI is less than WPI as shown by the various variance tools applied in the paper.

Modeling and Predicting Exchange Rate Volatility: Application of Symmetric GARCH and Asymmetric EGARCH and GJR-GARCH Models

La modélisation et la prévision de la volatilité sont devenues de plus en plus importantes ces derniers temps étant donné qu’une compréhension de la volatilité future peut aider les investisseurs et les diverses parties prenantes à minimiser leurs pertes. Cet article applique l’analyse de séries chronologiques univariées dans la modélisation et la prédiction de la volatilité des taux de change entre le FCFA Camerounais (XAF) et le Dollar Américain (USD) et entre le FCFA Camerounais et le Yuan Chinois (CNY). En utilisant les prix de clôture quotidiens du 1er Janvier 2017 au 30 Septembre 2022, les modèles d’hétéroscédasticité conditionnelle autorégressive généralisée symétrique (GARCH) et asymétrique GARCH exponentiel (EGARCH) et Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) sont utilisés pour capturer des faits stylisés sur l’échange rendements des taux. Les ensembles de données dans l’échantillon et hors échantillon contiennent des données du 1er Janvier 2017 au 31 Décembre 2021 et du 1er Janvier 2022 au 30 Septembre 2022 respectivement. Les résidus sont supposés suivre les distributions normale, t et d’erreur généralisée avec leurs homologues asymétriques. En considérant le modèle avec les critères d’information d’Akaike (AIC) les plus bas, l’article trouve ARMA (0,1) + GJRGARCH (1,1) - SGED et ARMA(1,1)+GJR-GARCH(2,2) - SGED comme les modèles les plus appropriés pour décrire la volatilité des rendements des taux de change USD/XAF et CNY/XAF respectivement. De même, ARMA(0,1)+GARCH(1,1) - SGED et ARMA(1,1)+GJR-GARCH(2,2)-SGED sont les meilleurs modèles prédictifs hors échantillon pour la volatilité de taux de change USD/XAF et CNY/XAF utilisent respectivement l’erreur absolue moyenne (MAE) et l’erreur quadratique moyenne (RMSE). Les effets de levier caractérisent le taux de change CNY/XAF mais sont absents des données sur le taux de change USD/XAF. Les résultats montrent que les modèles hétéroscédastiques conditionnels peuvent être utilisés efficacement pour modéliser et prédire la volatilité conditionnelle des séries de taux de change. Cette recherche recommande que, dans la conception de politiques de taux de change appropriées, les autorités monétaires Camerounaises et la BEAC prennent en considération le fait que le marché des taux de change est très volatil et réagit différemment aux bonnes comme aux mauvaises nouvelles. Modeling and predicting volatility has become increasingly important in recent times given that an understanding of future volatility can help investors and various stakeholders to minimize their losses. This paper applies univariate time series analysis in the modeling and prediction of the volatility of the exchange rates between Cameroon’s FCFA (XAF) and the US Dollar (USD) and between Cameroon’s FCFA and the Chinese Yuan (CNY). Using daily closing prices from 01 January 2017 to 30 September 2022, both symmetric Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and asymmetric Exponential GARCH (EGARCH) and Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) models are used to capture stylized facts about exchange rate returns. The in-sample and out-of-sample data sets contain data from 01 January 2017 to 31 December 2021 and from 01 January 2022 to 30 September 2022 respectively. The residuals are assumed to follow the normal, student’s t and generalized error distributions along with their skewed counterparts. Considering the model with the lowest Akaike Information Criteria (AIC), the paper finds ARMA(0,1) + GJR-GARCH(1,1) - SGED1 and ARMA(1,1)+GJR-GARCH(2,2) - SGED as the most appropriate models to estimate the volatility of the USD/XAF and CNY/XAF exchange rate returns respectively. Equally, ARMA(0,1)+GARCH(1,1) - SGED and ARMA(1,1)+GJR-GARCH(2,2)-SGED are the best out-of-sample predictive models for the volatility of the USD/XAF and CNY/XAF exchange rate returns respectively using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Leverage effects are found to characterize the CNY/XAF exchange rate but absent in the USD/XAF exchange rate data. The results show that conditional heteroscedastic models can be effectively used to model and predict the conditional volatility of exchange rate series. This research recommends that, in the design of appropriate exchange rate policies, Cameroon’s monetary authorities and BEAC should take into consideration the fact that the exchange rate market is very volatile and reacts differently to both good and bad news.

Spillover and portfolio analysis for oil and stock market: A new insight across financial crisis, COVID-19 and Russian-Ukraine war

This research examines the link between the volatility of the Karachi Stock Exchange and West Texas Intermediate (WTI) crude oil, using daily data between July 1, 2001 and December 31, 2022. We further investigate the spillover and investment strategies variation across the financial crisis, COVID-19, and the Russian-Ukrainian conflict. We employ the well-known investment analysis; portfolio weights, hedge ratio and hedging effectiveness. We extract the estimates from symmetric and asymmetric GARCH approaches for investment analysis. Asymmetric GARCH provides the response of negative and positive shocks. The findings demonstrate that lagged volatility, rather than lagged shocks, is a better predictor of market volatility in the future. Furthermore, the data support the notion that shocks, and volatility are communicated for the case of before, during, and after the crisis. After the outbreak of COVID-19 and the subsequent Russian-Ukraine war, researchers have discovered a transmission of shock and volatility from oil to stock markets. For policy suggestions, we recommend that oil revenue might be used to cushion other investment losses. After COVID-19 and the Russian-Ukraine war, investors should buy oil assets to hedge their portfolios against the ensuing catastrophe. However, the policy suggestions arising from the study findings may be employed by investors and portfolio managers.

Bitcoin, Gold and Crude Oil versus the US Dollar – A GARCH Volatility Analysis

Abstract The aim of this study is to compare and contrast the volatility of different asset classes namely Bitcoin, gold and crude oil against the US dollar, using the symmetric GARCH (1,1) model. Furthermore, this study examines which of the three assets provide the lowest volatility and identifies if the univariate GARCH (1,1) model can suitably forecast the volatility of the foreign exchange market, commodity market and cryptocurrency market. More specifically, this study uses only estimates from a symmetric GARCH model for the XAU/USD, WTI/USD and BTC/USD financial assets. Although the literature on the volatility of different assets is extensive, it neglects to detect the severe economic recession that is approaching. Considering that powerful nations purchased substantial quantities of gold in order to back their national currency, supremacy of the US dollar is under significant attack. Experts in international relations have claimed that it is essential to have a single, extremely influential national economy to exhibit stability and operate smoothly. Specifically, the international monetary system functioned under the theory of hegemonic stability. Given the fact that gold still remains the safe haven asset during periods of financial and economic distress, central banks are purchasing gold at a rapid pace with Russia and China leading the way. Furthermore, the demand for precious metals has also increased while the US dollar is struggling to keep its supremacy as BRICS reserve currency is seeking to replace it in the future. The daily data encompassing the necessary information for February 2012 - February 2020 is acquired from “Investing.com”, reaching 7193 observations. This study will enrich the literature associated with volatility forecasting of different asset classes during financial and economic turmoil while also raising awareness of the economic threats that could follow.

Application of GARCH models in the volatility of food inflation in Nigeria

This paper aimed to investigate the behavior of the current food inflation volatility arising from the recent past behavior and to know if this volatility is persistent over time in Nigeria. The study covered the period from 2003M1 to 2021M9 under both the asymmetric and the symmetric GARCH models. The findings of the study revealed that one period lag of food inflation had a positive and significant impact on the current value of food inflation. Furthermore, it was found that in all the selected models, volatility in food inflation is persistent and bad news had an impact on food volatility in two of the models, while good news had an impact in one model. However, the asymmetric coefficient in all the asymmetric models is not significant. Consequently, the study contends that policymakers should factor in the impact of recent past values of inflation when framing policies meant to tame food inflation in Nigeria. Keywords: Asymmetric models, GARCH models, inflation, volatility;

Symmetric and asymmetric GARCH estimations of the impact of oil price uncertainty on output growth: evidence from the G7.

Crude oil is an essential source of energy. Without access to energy, output growth is impossible. As a result of this link, volatility in oil prices has the ability to induce fluctuations in the output of both developed and developing economies. Moreover, factors such as business cycles and policy changes often introduce nonlinearity into the transmission mechanism of oil price shocks. This study therefore examines not only the interconnectedness of oil price volatility and output growth, but also the nonlinear, asymmetric impact of oil price volatility on output growth in the countries making up the Group of Seven. To this end, monthly data on West Texas Intermediate oil price and industrial production indices of the Group of Seven countries over the period 1990:01 to 2019:08 is used for empirical analysis. The study employs the DCC and cDCC-GARCH techniques for symmetric empirical analysis. The asymmetric empirical analysis is also conducted via GJR-GARCH, FIEGARCH, HYGARCH and cDCC-GARCH techniques. The findings reveal disparities in the magnitudes of the positive and negative (asymmetric) effects of oil price shocks on output growth. The results also reveal that past news and lagged volatility have a significant impact on the current conditional volatility of the output growth of the Group of Seven countries. The study concludes that the impact of oil price volatility on output growth in the selected economies is asymmetric, the volatility is highly persistent and clustered, and the asymmetric GARCH models outperform the symmetric GARCH models.

Stock Returns Volatility in Nepal: Evidence during Covid-19

This study scrutinizes the stock returns volatility pattern in Nepal during the COVID-19 period from March 3, 2020 to February 27, 2022. By examining GARCH family models with Generalized Error Distribution specification, the results of symmetric GARCH models show that there is persistent volatility in daily stock returns in Nepal over the study period. The observed persistent volatility in daily stock returns indicate that the current shocks in daily stock returns exist in forecasting variance for longer period in future. The results of asymmetric TGARCH (1, 1) model show that there is the leverage effects on the volatility of daily stock returns in Nepal during the study period. The observed leverage effects implies that uncomplimentary news have larger effects on the volatility than the complimentary news of the same intensity. Finally, results establish the GARCH (1, 1) model as the best fitted symmetric model to explain the volatility persistence and the TGARCH (1,1) model as the best fitted asymmetric models to predict the leverage effects on the time varying conditional volatility of daily stock in Nepal. The main implication of findings from this study is that it offers an additional insight to form sound investment strategy to address risk structure of Nepali stock market.

An Analysis of the Exchange Rate Volatility in Poland using the GARCH, GJR-GARCH and EGARCH Models

This paper employs the symmetric GARCH and the asymmetric GJR-GARCH(1,1) and E-GARCH(1,1) models to explain the dynamics of the PLN/EUR and PLN/USD exchange rates in Poland for the periods of January 2015 to July 2022. The result of our study shows that the USD rate is more susceptible to market fluctuations and events than the EUR rate. Additionally, both rates' volatility persists after a market crisis for a while, with the EUR rate taking longer until volatility subsides. Using the Akaike information criterion and Bayesian information criterion, we find the E-GARCH model to be the best model out of all three models considered.

GARCH-M MODEL AND THE BEHAVIOR OF RISK-RETURN RELATIONSHIP IN INDONESIA STOCK MARKET

This study examines the risk-return trade-off and volatility behaviour in Indonesia stock market. As the analytical tool this study uses GARCH-M model with symmetric GARCH(1,1). To obtain more reliable results, this study takes daily and weekly stock index as well as 5 individual stock returns from January 2004 to November 2020 as a sample. This study also investigates the results with two alternative mean equations, simple regression and AR(1) model. The first finding of this study is that in Indonesia stock market both in stock index and in individual stocks, the volatilities of return are time varying. From investigating the risk-return relationship the results are mixed. This study finds that positive risk-return relationships in stock market index are observed both in daily and weekly data. A positive risk-return relationhip in stock market index is also found either in AR(1) model of mean equation or in simple regression model. The same results are observed in two stocks investigated. There is one stock where a positive risk return relationship is observed only in daily return data not in weekly return data. A negative risk-return relationships is observed in one stock and there is no evidence of risk-return trade-off in one stock. The conclusion is that a positive risk-return relationship as a postulated by investment theory only exists in stock index and does not exist in all stocks
 
 Key words : Indonesia stock market, Risk-return trade-off, GARCH-M, GARCH(1,1), Time-varying volatility.

Global and Country-Specific Geopolitical Risks and Exchange Rate Volatility: New Empirical Evidence from Indonesia

This paper investigates the conditional predictability of geopolitical risks (GPR) on the rupiah-dollar exchange rate volatility, using 447 monthly observations spanning January 1985 to March 2022. The paper utilizes asymmetric GARCH (1,1) combined with various asymmetric GARCH models, including the integrated GARCH (I-GARCH), the exponential GARCH (E-GARCH), and the threshold GARCH (T-GARCH), and the power asymmetric GARCH (A-PARCH). This study finds convincing evidence that GPRI has a consistent effect on exchange rate volatility, either symmetric GARCH models or asymmetric GARCH models. Interestingly, the global geopolitical risks (GPR) heterogeneously affect the exchange rate volatility of Indonesia. These empirical findings imply that the rupiah-dollar exchange rate volatility is more vulnerable to domestic GPRI than global GPR.

The influence of different financial market regimes on the dynamic estimation of GARCH volatility model parameters and volatility forecasting

Volatility is one of the measures of risk within the financial markets. GARCH modelling involves important volatility forecasting methodology and is widely used in finance. It is important to be able to forecast volatility since volatility has an impact on financial portfolios and the risk hedging methodology followed by financial companies. This study investigates the behaviour of parameter estimates and volatility forecasts of GARCH models over time, using a rolling window estimation procedure. Three GARCH models, the Symmetric GARCH, GJR-GARCH and E-GARCH models, are compared. The dataset used in the study comprises of the JSE All-Share index. This index is divided into two different periods, namely, a tranquil financial period and a turbulent financial period. Different factors influence the performance of GARCH models and consequently determines which GARCH model is the most suited for certain circumstances. These factors are: the sample window period, forecasting horison, the financial period and the underlying distribution of the log returns.

Managing Exchange Rate Volatility during Political Crises

The goal of this paper is to show how the exchange rate volatility could be managed during political crises, using as a case study the fragile
 the political relationship between USA and Turkey between 2014-2019. The Turkish Lira has dramatically dropped against the US dollar to a record low level in August 2018. The Turkish president accused the American president of economic war, insisting that his country would survive an economic assault, but neglecting to comfort financial markets (worried about the breakdown of the national currency of a crucial emerging economy). Meanwhile, investors feared that a financial crisis could spread throughout Europe. Fears of contagion remained high, although the central bank of Turkey pledged to provide liquidity for Turkish banks. In this background, this paper tries to find if different specifications of univariate GARCH models can anticipate volatility in the foreign exchange market. Our study uses estimates from a symmetric GARCH model, namely GARCH (1,1) for the TRY/USD exchange rate. The data set was obtained from “Investing.com” and covers
 the period January 2014 – to October 2019. This study shows that GARCH (1, 1) can be successfully applied in modeling and forecasting the volatility trend of the currencies and so in exchange rate administration.

Modeling and Forecasting the Volatility of NIFTY 50 Using GARCH and RNN Models

The stock market is constantly shifting and full of unknowns. In India in 2000, technological advancements led to significant growth in the Indian stock market, introducing online share trading via the internet and computers. Hence, it has become essential to manage risk in the Indian stock market, and volatility plays a critical part in assessing the risks of different stock market elements such as portfolio risk management, derivative pricing, and hedging techniques. As a result, several scholars have lately been interested in forecasting stock market volatility. This study analyzed India VIX (NIFTY 50 volatility index) to identify the behavior of the Indian stock market in terms of volatility and then evaluated the forecasting ability of GARCH- and RNN-based LSTM models using India VIX out of sample data. The results indicated that the NIFTY 50 index’s volatility is asymmetric, and leverage effects are evident in the results of the EGARCH (1, 1) model. Asymmetric GARCH models such as EGARCH (1, 1) and TARCH (1, 1) showed slightly better forecasting accuracy than symmetric GARCH models like GARCH (1, 1). The results also showed that overall GARCH models are slightly better than RNN-based LSTM models in forecasting the volatility of the NIFTY 50 index. Both types of models (GARCH models and RNN based LSTM models) fared equally well in predicting the direction of the NIFTY 50 index volatility. In contrast, GARCH models outperformed the LSTM model in predicting the value of volatility.

GARCH pricing and hedging of VIX options

AbstractWe are the first to study the pricing and hedging of VIX options via Monte Carlo (MC) under GARCH(1,1) and Glosten–Jagannathan–Runkle GARCH(1,1) models. Our pricing is ab initio and out‐of‐sample and can be implemented in real time. Importantly, we propose the so‐called single‐option hedge error, a better measure than that of Bakshi et al., and suggest several techniques to expedite MC by over 1000 times, which rivals the potential speedup of quantum computers. Empirically, our proposed approach outperforms two types of benchmarks; further, the asymmetric Glosten–Jagannathan–Runkle outperforms the symmetric GARCH. Overall, our paper has both theoretical and practical implications.

High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model

Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.

Forecasting volatility in Asian financial markets: evidence from recursive and rolling window methods

The present paper examines the relative out-of-sample predictive ability of GARCH, GARCH-M, EGARCH, TGARCH and PGARCH models for ten Asian markets by using three different time frames and two different methods, considering the features of volatility clustering, leverage effect and volatility persistence phenomena, for which the evidence of existence is found in the data. Five measures of comparison are employed in this research, and a further dimension is investigated based on the classification of the selected models, in order to identify the existence or lack of any differences between the recursive and rolling window methods. The empirical results reveal that asymmetric models, led by the EGARCH model, provide better forecasts compared to symmetric models in higher time frames. However, when it comes to lower time frames, symmetric GARCH models tend to outperform their asymmetric counterparts. Furthermore, linear GARCH models are penalized more by the rolling window method, while recursive method places them amongst the best performers, highlighting the importance of choosing a proper approach. In addition, this study reveals an important controversy: that one error statistic may suggest a particular model is the best, while another suggests the same model to be the worst, indicating that the performance of the model heavily depends on which loss function is used. Finally, it is proved that GARCH-type models can appropriately adapt to the volatility of Asian stock indices and provide a satisfactory degree of forecast accuracy in all selected time frames. These results are also supported by the Diebold-Mariano (DM) pairwise comparison test.