Symmetric GARCH Research Articles

Time-varying ARFIMA-GARCH model with symmetric thresholds: applications to inflation

ABSTRACT This study suggests a structural modification of the basic ARFIMA-GARCH model by allowing for time-varying baseline mean and, especially, symmetric threshold GARCH. By applying it to the inflation of G7 countries, we find that past excessive positive or negative shocks have positive impacts on future volatility and GARCH persistence. Compared with the ARFIMA-GARCH model, the model in this study has superior performances in identifying and characterizing structural changes and excessive shocks.

Does Borsa Istanbul incorporate herding and calendar anomalies an empirical evidence

Purpose- Anomalies and herding rather than individual rational decisions could be detected in capital markets. Such formations’ enabling abnormal returns under volatility, may be of interest in respect of Turkish capital markets. This study analyzes the herd behavior and calendar anomalies in Borsa Istanbul (BIST) by generalizing the main index and the sectoral indices. Methodology- The data set is based on the weekly closing prices, trading volume and the number of contracts of BIST-100 Index and 17 sectoral indices for the January 2012 to December 2016. A symmetric GARCH (1,1) and an asymmetric SAARCH (1,1) models have been employed for a comparative analysis. Findings- Since GARCH (1,1) findings revealed a quiet weak simultaneous interaction between volatility and return, the research was deepened through employment of the SAARCH (1,1) asymmetric estimation model, which revealed an increase in both trading volume and return when considering negative shocks. Hence, a significant herding in BIST has been confirmed. SAARCH (1,1) model has detected day of the week (DoW) and a significant January effect, as well, while both estimation models have detected Ramadan effects. Conclusion- It becomes apparent that there is a gap in the Turkish capital market-related combined studies on herding and calendar anomalies. The aim of this study, therefore, is to fill this gap, using analyses of the BIST-100 and sectoral indices. Main indices, consisting of blue-chips, are analyzed frequently; however, abnormal trading behaviors could be detected specifically on sectoral basis.

Modeling and Forecasting USD/UGX Volatility through GARCH Family Models: Evidence from Gaussian, T and GED Distributions

Symmetric and asymmetric GARCH models-GARCH (1,1); PARCH(1;1); EGARCH(1,1,); TARCH(1,1) and IGARCH(1,1)- were used to examine stylized facts of daily USD/UGX return series from September 1st, 2005 to August 30th, 2018. Modeling and forecasting were performed based on Gaussian, Student's t and GED distribution densities with a view to identifying the best distribution for examining stylized facts about the volatility of returns. Initial tests of heteroscedasticity (ARCH-LM), autocorrelation and stationarity were carried out to establish specific data requirements before modeling. Results for conditional variance indicated the presence of significant asymmetries, volatility clustering, leptokurtic distribution, and leverage effects. Effectively, PARCH (1,1) under GED distribution provided highly significant results free from serial correlation and ARCH effects, thus revealing the asymmetric responsiveness and persistence to shocks. Forecasting was performed across distributions & assessed based on symmetric lost functions (RMSE, MAE, MAPE & Thiel's U) and information criteria (AIC, SBC & Loglikelihood). The information criteria offered a preference for EGARCH (1,1) under GED distribution while symmetric lost functions provided very competitive choices with very slight precedence for GARCH (1,1) and EGARCH (1,1) under GED distribution. Following these results, it's recommended that PARCH (1,1) and EGARCH (1,1) be respectively preferred for modeling and forecasting volatility with GED as the choice distribution. Given the asymmetric responsiveness and persistence of conditional variance, macroeconomic & fiscal adjustments in addition to stabilization of the internal political environment are advised for Uganda. Keywords: Forecasting volatility, GARCH family Models, Probability Distribution Density, Forecast accuracy.JEL Classifications: C58, C53, G17, F31DOI: https://doi.org/10.32479/ijefi.9016

Forecasting of the Nigeria Stock Returns Volatility Using GARCH Models with Structural Breaks

This study examines the stock returns series using Symmetric and Asymmetric GARCH models with structural breaks in the presence of some varying distribution assumptions. Volatility models of Symmetric GARCH (1,1), Asymmetric Power GARCH (1,1) and GJR-GARCH(1,1) models were considered in estimating and measuring shock persistence, leverage effects and mean reversion rate with structural breaks considering dummy variable for these structural changes and varying distributions . The skewed student-t distribution is considered best distribution for the models; moreover findings showed the high persistence of shock in returns series for the estimated models. However, when structural breaks were incorporated in the estimated models by including dummy variable in the conditional variance equations of all the models, there was significant reduction of shock persistence parameter and mean reversion rate. The study found the GJR-GARCH (1,1) with skewed student-t distribution best fit the series. The volatility was forecasted for 12 months period using GJR-GARCH (1,1) model and the values are compared with the actual values and the results indicates a continuous increase in unconditional variance.

Modelling the oil price volatility and macroeconomic variables in South Africa using the symmetric and asymmetric GARCH models

This article employed the ARCH, GARCH and EGARCH models to model the oil price volatility and macroeconomic variables in South Africa for the period 1990Q1 to 2018Q2. The macroeconomic variables used in the study are GDP, inflation, interest rate and exchange rates. According to ARCH (1) and GARCH (1, 1) models, exchange rate and interest rate have a negative effect on the oil price, while GDP and inflation suggesting a positive effect. The results for GDP and inflation imply that a 1% increase in GDP and inflation may lead to an increase in oil price. The negative effect on interest rate and exchange rate led by their negative values implies that a 1% increase in interest rate and exchange rate may lead to a decrease in oil price. The EGARCH (1, 1) model revealed that oil price is negatively affected by all the macroeconomic variables. This implies that a 1% increase in these variables may lead to a decrease in oil price. The symmetric and asymmetric techniques revealed that the South African oil prices are volatile. The article recommends that South African policy makers should have a view on the impact of oil price volatility on the South African economy.

Volatility Modelling of Global Financial Crises Effects on the Nigerian Banks

The most appropriate heteroskedastic models for predicting volatility of daily stocks prices of 10 major Nigerian banks are proposed. The banks are Access, United Bank for Africa (UBA), Guaranty Trust, Skye, Diamond, Fidelity, Sterling, Union, ETI and Zenith banks; and these are examined from 2004 to 2014. The models employed are Autoregressive Conditional Heteroscedastic (ARCH(1)), Generalized Autoregressive Conditional Heteroscedastic (GARCH(1, 1)), Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH(1, 1)) and Glosten, Jagananthan and Runkle-Generalized Autoregressive Conditional Heteroscedastic (GJR-GARCH(1, 1)). The results show that all the bank returns are highly leptokurtic, significantly skewed and thus non-normal across the four periods except for Fidelity bank during financial crises; findings similar to those of other global markets. Also noticed is the strong evidence for the presence of heteroscedasticity, and that volatility persistence during crisis is higher than before the crisis across the 10 banks, with that of UBA taking the lead, about 11 times higher during the crisis. The same with persistence levels in volatility, which were relatively higher during financial crises across the ten banks compared to before the crises. Findings further indicate that Asymmetric GARCH models outperformed the symmetric GARCH models, especially during the financial crises and post the crises. Thus with these findings, one could generally conclude that Nigerian banks’ returns are volatility persistent during and after the crises, and are characterized by leverage effects of negative and positive shocks during these periods.

Efficient Out-of-Sample Pricing of VIX Futures

The authors propose the first closed-form price formulas for VIX futures under the widely used discrete-time symmetric GARCH(1, 1) and asymmetric Glosten–Jagannathan–Runkle (GJR) GARCH(1, 1) models. For VIX futures expired before July 21, 2017, the proposed methods, which are truly simple, perform reasonably well in out-of-sample pricing. In regard to pricing errors and efficiency, the new methods significantly outperform a continuous-time benchmark based on the Heston volatility model and a discrete-time benchmark based on the Heston–Nandi GARCH(1, 1). Empirically, GJR is the most “potent”—a term the authors apply to the ability of the model to successfully price VIX futures in the data set. The GJR potency in this study is as high as 96.6%. The novel GARCH approaches are unique with the implication of applicability in real time. Finally, an insight is gained into the research of pricing, namely, that potency is an important gauge of a pricing method. TOPICS:Futures and forward contracts, derivatives, factor-based models Key Findings • Closed-form price formulas for VIX futures under GARCH(1,1) and GJR GARCH(1,1) models are proposed. • The novel approaches are shown to be really competitive for out-of-sample, and more importantly imply applicability in real time, pricing of VIX futures. • Potency, as a gauge of the success rate of pricing, is proposed.

Assessing the risk of the European Union carbon allowance market

Purpose The purpose of this paper is to examine the impact of structural breaks on the conditional variance of carbon emission allowance prices. Design/methodology/approach The authors employ the symmetric GARCH model, and two asymmetric models, namely the exponential GARCH and the threshold GARCH. Findings The authors show that the forecast performance of GARCH models improves after accounting for potential structural changes. Importantly, we observe a significant drop in the volatility persistence of emission prices. In addition, the effects of positive and negative shocks on carbon market volatility increase when breaks are taken into account. Overall, the findings reveal that when structural breaks are ignored in the emission price risk, the volatility persistence is overestimated and the news impact is underestimated. Originality/value The authors are the first to examine how the conditional variance of carbon emission allowance prices reacts to structural breaks.

MODELING AND FORECASTING EXCHANGE RATE VOLATILITY IN EEC COUNTRIES

This main objective of this paper is to examine the properties of the GARCHmodel and its usefulness in modeling and forecasting the volatility of exchange ratemovements in selected EEC countries (Romania, Hungary and Serbia). The dailyreturns of exchange rates on Hungarian forint (HUF), Romanian lei (ROL) andSerbian dinar (RSD), all against the US dollar are analyzed during the period 03.January 2000 to 15. April 2013 in respect. In order to measure the involved risk,symmetric and asymmetric GARCH models are applied. The accuracy of exchangerate volatility forecast is evaluated through reference to the most commonly usedcriteria. These include a Mincer-Zarnowitz regression based test, Mean AbsoluteError (MAE), Root Mean Square Error (RMSE) and Diebold and Mariano test (DMtest). The results of Mincer-Zarnowitz regression test for selected exchange ratereturn series showed a clear lack of explanotory power and sub-optimality of theTGARCH model. The results of the Mean Absolute Error (MAE) and the Root MeanSquare Error (RMSE) for the forecasted volatility showed that symmetric modelbetter predict conditional variance of the exchange rate returns, but estimating resultsindicating that the parameters of forecasts are not satisfactory, i.e. models have littlepredictive power. Results for Diebold-Mariano test results for Diebold-Mariano testshowed that symmetric model outperforming TGRACH forecast in case of Hungarianforint and Serbian dinar sample series, and that only in case of Romania lei TGARCHoutperforming the GARCH forecast.

Symmetric and Asymmetric GARCH Estimations and Portfolio Optimization: Evidence From G7 Stock Markets

Volatility exchanges between equity markets and oil markets are vital for portfolio designing and risk management. This study empirically analyses the interdependence of stock and oil market for G7...

Modeling and Forecasting the Volatility of Gasoline Prices Using Symmetric and Asymmetric GARCH Models in Erbil City

The paper aims to compare the performance of several univariate symmetric and asymmetric GARCH volatility models in modeling and forecasting the volatility of daily Gasoline prices in Erbil city. This paper chooses the GARCH, GARCH-M, TGARCH, E-GARCH and Power GARCH model to analyze the daily return of Gasoline under three different error distributions: normal distribution, student-t distribution and generalized error distribution and then compare the results and choose the appropriate model to forecast the volatility. The sample is divided into two subsamples. The first subsample is called in-sample data set (Training sample) used to estimate the ARMA-GARCH models for underlying data and the second subsample is called out-sample data set (Testing sample) used to investigate the performance of volatility forecasting. As a result of analyses, we conclude that the best model fits the volatility of Gasoline returns series is AR(2)-Power GARCH(2,1,1) non-linear asymmetric model with innovation student-t distribution (d.f =10), and has better forecasting performance than others models. This result is important in many fields of finance such as investment decisions, asset pricing, portfolio allocation and risk management. Keywords : Conditional Variance; Volatility Clustering; Symmetric and Asymmetric GARCH Models; Error Distribution; Volatility Forecasting; Root Mean Square Error (RMSE)

Modeling Volatility of Asset and Volume of Trade Returns in the Nigerian Stock Market in the Presence of Random Level Shifts

This study investigated the impact of volatility shock persistence on the conditional variance in the Nigerian stock returns using symmetric and asymmetric higher order GARCH family models in the presence of random level shifts and non-Gaussian errors. The study utilised Bai and Perron methodology to detect structural breakpoints in the conditional variance of daily stock and volume of trade returns in the Nigerian stock market from 2nd January, 1998 to 22nd March, 2017. The study employed symmetric GARCH (3,2) and GARCH (2,1)-M models to estimate volatility of asset returns, symmetric GARCH (2,2) and GARCH (2,1)-M to model volatility of volume of trade returns and asymmetric EGARCH (2,2), TGARCH (3,2) and PGARCH (2,3) models to measure the volatility of asset returns as well as asymmetric EGARCH (2,1), TGARCH (1,3) and PGARCH (3,2) models to estimate volatility of volume of trade returns. These models were optimally selected using information criteria and log likelihood as the best fitting symmetric and asymmetric GARCH models to estimate the conditional volatility of asset and volume of trade returns in the Nigerian stock market with and without structural breaks. Results revealed that when random level shifts were ignored in volatility models, the shocks persistence were very high with long memory and variance explosion. But when the random level shifts were incorporated into the GARCH models, there was a significant reduction in the volatility shocks persistence and long memory. Moreover, volatility half-lives also declined drastically while accounting for these sudden level shifts in variance. The study found asymmetry without leverage effects as well as a positive risk-return tradeoff for both asset and volume of trade returns in the Nigerian stock market. The Nigeria banking reform of 2004, the Global Financial and Economic Crises, as well as other local events in Nigeria, were found to have negative and significant impacts on the Nigerian stock market. The study provided some policy recommendations.

Modeling Volatility of Exchange Rates Returns in the Nigerian Foreign Exchange Market in the Presence of Non-Gaussian Errors

This study investigates volatility behaviour of exchange rates returns of Naira against CFA, Euro, Great British Pounds, US Dollar, West African Unit of Account (WAUA) and Japanese Yen in Nigeria using historical volatility approach as well as symmetric and asymmetric Autoregressive Conditional Heteroskedasticity (GARCH) models in the presence of non-Gaussian errors. The study utilizes daily quotations of these exchange rates from 12/11/2001 to 04/13/2018 making a total of 4008 observations each. Historical (annualized) volatility approach as well as symmetric GARCH (1,1) and asymmetric EGARCH (1,1) models were used to model the exchange rates return series. Results showed that CFA and USD have the highest and least annualized volatilities (market risk) respectively among the six exchange rates returns as measured by historical approach. The symmetric GARCH (1,1) model showed volatility clustering with evidence of shock persistence in the six exchange rates return series. The asymmetric EGARCH (1,1) model found evidence of asymmetry and leverage effects in the Nigerian foreign exchange market indicating that negative shocks (bad news) generate more volatility than positive shocks (good news) of similar magnitudes. All the estimated models were found to be stationary and mean reverting indicating the predictability and stability of the conditional variances of the foreign exchange rates returns. This result suggests that no matter how high or low the foreign exchange rates shall move in the exchange market, they shall eventually return to their long-run averages. Stationary and mean reverting stocks provide good and long term investment opportunities for investors.

Estimating Stock Returns Volatility and the Risk-Return Nexus in the Nigerian Stock Market in the Presence of Shift Dummies

Volatility and the trade-off between risk and return in stock markets is an important subject in financial theory which play significant role in investment decision making, portfolio selection, options pricing, financial stability, hedging and pair trading strategy among others. This study estimates stock return volatility and analyses the risk-return trade-off in the Nigerian stock market using symmetric GARCH (1,1)-in-mean, asymmetric CGARCH (1,1)-in-mean and EGARCH (1,1)-in-mean models with Generalized Error Distribution and Student-t innovation. Data on daily closing all share prices of the Nigerian stock exchange for the period 2nd January, 1998 to 9th January, 2018 are utilised. The data is further divided into three sub-periods of pre-crisis, global financial crisis and post crisis periods to allow volatility behaviour and the risk-return trade-off to be investigated across the sub-periods. Results showed evidence of volatility clustering, leptokurtosis, high persistence of shocks to volatility and asymmetry without leverage effects across the study periods. The persistence of shocks to volatility increased during the global financial crisis period with delayed reactions of volatility to market changes. However, by incorporating the exogenous breaks into the volatility models for the full study period, the shock persistence drastically reduced with faster reactions of volatility to market changes. The results of this study also found supportive evidence for a significant positive risk-return relationship in Nigerian stock market across various study sub-periods and model specifications meaning that investors in Nigerian stock market should be compensated for holding risky assets. The empirical findings of this study further suggest that the recent global financial crisis have not altered the market dynamics to distort the risk-return trade-off in Nigerian stock market indicating that expected returns are not driven by changes in the stock market volatility. The study provides some policy recommendations for investors and policy makers in the Nigerian stock market.

Intraday return volatility in Saudi Stock Market: An evidence from Tadawul All Share Index

The association between risk and return is a significant concept in finance that has been studied in the past to a large extent. The stock market volatility is closely associated with the risk. The current study examines the intraday volatility pattern of stock market of Saudi Arabia by reviewing the stocks of Tadawul All Share Index (TASI). We obtain return data at 5-minute frequency from the SASEIDX starting on 25 October 2017 and ending on 9 May 2018. We examine the stock market volatility by using different symmetric and asymmetric GARCH models and observe that, the symmetric GARCH models showed a significant positive association between risk and return. Similarly, the asymmetric GARCH models show that the estimates were significant and the leverage estimate was negative and significant, indicating a no-leverage effect in the return series. Moreover, the asymmetric results suggest that negative shocks do not entail to future higher volatility than positive shocks. Therefore, the symmetric and asymmetric GARCH models are comfortable to capture the volatility of Saudi stock market from Intraday data.

Modelling and forecasting long memory time series with Exponential and Switching GARCH models

There is some evidence that structural change or stochastic regime switching and long memory are intimately related concepts. However, long memory and regime switching in a stochastic process are properties that could be easily confused in a financial study. Using a modelling approach, the aim is to distinguish regime switching behaviour from long memory for the financial time series. In an empirical study the forecasting performance of symmetric, asymmetric, long memory and Markov switching GARCH model are compared using Tehran stock market daily returns. The results indicate that in out of sample performance, long memory exponential GARCH (FIEGARCH) model outperforms the competing models. To ensure the validity of the results, the value at risk (VaR) forecasts are obtained for each model and a loss function is calculated. A simple rule for distinguishing between long memory and structural break in financial and economic time series is suggested.

The accuracy of asymmetric GARCH model estimation

This paper reviews eight software packages when estimating asymmetric GARCH models (from their default option). We consider the numerical consistency of GJR-GARCH, TGARCH, EGARCH and APARCH estimations with Normal and Student distributions as well as out-of-sample forecasting accuracy, using the model confidence set procedure. We show that results are clearly software-dependent for both asymmetric volatility models, especially for the t-ratios. The out-of-sample forecast results show that the differences in estimating symmetric and asymmetric GARCH models imply slight differences in terms of forecast accuracy, not statistically significant, except in few cases from the QLIKE loss function. Further, the results indicate that the different specifications of the asymmetric GARCH-type models used by the different packages appear to have no significant effect on their forecast accuracy.

Respon Return Pasar Modal Indonesia terhadap Kebijakan Moneter Domestik dan Asing

Understanding the impact of external shocks on the stock market return and volatility is crucial for market participants as volatility is synonymous with risk. This paper provides comprehensive evidence on the spillover effects of the change of monetary policies from inside country and foreign origins on Indonesia stock market in the period of the time from November 2, 2012 to May 15, 2017. Used symmetric (IGARCH) and asymmetric (EGARCH and APARCH) GARCH model analysis to evaluate the impact of surprise and anticipated changes of monetary policies from inside country and foreign policies (from another ASEAN countries and leading economies, in this paper are United States, Europe, and United Kingdom). Surprise change of monetary policy is proxied by one day change in 3 months interbank offered rate, while anticipated change of monetary policy is proxied by one day change in target interest rate or policy rate. The result shows that information of the monetary policy news and Indonesia stock return is asymmetric. Indonesia stock market is only affected by foreign monetary policies. Keywords: ASEAN stock market, GARCH, Monetary policy JEL classification: C01, C50, E50

Respon Return Pasar Modal Indonesia terhadap Kebijakan Moneter Domestik dan Asing

Understanding the impact of external shocks on the stock market return and volatility is crucial for market participants as volatility is synonymous with risk. This paper provides comprehensive evidence on the spillover effects of the change of monetary policies from inside country and foreign origins on Indonesia stock market in the period of the time from November 2, 2012 to May 15, 2017. Used symmetric (IGARCH) and asymmetric (EGARCH and APARCH) GARCH model analysis to evaluate the impact of surprise and anticipated changes of monetary policies from inside country and foreign policies (from another ASEAN countries and leading economies, in this paper are United States, Europe, and United Kingdom). Surprise change of monetary policy is proxied by one day change in 3 months interbank offered rate, while anticipated change of monetary policy is proxied by one day change in target interest rate or policy rate. The result shows that information of the monetary policy news and Indonesia stock return is asymmetric. Indonesia stock market is only affected by foreign monetary policies. Keywords: ASEAN stock market, GARCH, Monetary policy JEL classification: C01, C50, E50

Unravelling the Cipher of Indian Rupee’s Volatility: Testing the Forecasting Efficacy of the Rolling Symmetric and Asymmetric GARCH Models

Modelling exchange rate volatility is crucially important because of its diverse implications on the profitability of corporations and decisions of policy makers. This paper empirically investigates exchange rate volatility of India’s currency by applying rolling symmetric and asymmetric GARCH models to the USDINR and EURINR daily exchange rates for a period spanning April 1, 2006 through January 31, 2018, resulting in total observations of 2861. To estimate GARCH (1,1) and EGARCH (1,1) models, the data window is rolled over five years with nearly 1200 observations and one month is used as forecast period for each window. Both, in-sample criteria like the log likelihood criteria, Akaike information criterion (AIC), the Bayesian information criterion (SIC) and Hannan Quinn criterion (HQC) as well as the out-of-sample criteria like Mean Squared Error (MSE) and Mean Absolute Error (MAE) have been used to test model fit and forecast accuracy of the models. To test the robustness of the findings, Diebold-Mariano test is used to compare the predictive accuracy of both the models. Further, the forecasting accuracy of the two models has also been tested by splitting the sample period into periods of tranquility and volatility in Indian exchange rate. Results show that GARCH (1,1) model with generalized error distribution is adequate to capture the mean and volatility process of USDINR and EURINR exchange rate returns.