Symmetric GARCH Models Research Articles

Price discovery in the volatility index option market: A univariate GARCH approach

In this paper, the GARCH option pricing model is applied to the Standard and Poor’s 500 (S&P500) Volatility Index (VIX) option pricing. The purpose is to determine whether the GARCH option pricing model can be used for price discovery in the volatility index option market. The different GARCH models are fitted to VIX futures returns. The pricing performance is tested by comparing the option prices implied by the models to market option prices. The results show that the symmetric GARCH model with skewed Student-t errors is the best performing model, and that the GARCH option pricing model provides reasonable price discovery when applied to the VIX.

Choosing the Best Performing Garch Model for Sri Lanka Stock Market by Non-Parametric Specification Test

This paper examines the performance of different kind of GARCH models with Gaussian, Student-t and generalized error distribution for Colombo Stock Exchange (CSE), in Sri Lanka. Analyzing the daily closing price index of CSE from January 02, 2007 to March 10, 2013. It was found that the Asymmetric GARCH models give better result than symmetric GARCH model. According to distributional assumption these models under Student-t as well as generalized error provided better fit than normal distributional assumption. The Non-Parametric Specification test suggest that the GARCH, EGARCH, TARCH and APARCH models with Student-t distributional assumption are the most successful model for CSE.

Estimating Return Volatility of Stock Market Indices: The Case of Boursa Kuwait

This study empirically investigates the conditional variance (volatility) in the daily returns of Boursa Kuwait’s market index, along with seven sectoral indices, for the period of 13 May 2012 to 1 March 2018. The returns results exhibited leptokurtosis, were skewed left, and were not normally distributed; additionally, there was evidence of ARCH effects. The symmetric GARCH model results demonstrated evidence of volatility clustering and persistence; the GARCH-M model results showed a negative relationship between the indices’ returns and risk. The conditional variance (volatility) is affected by positive shocks, leading to positive asymmetric values of EGARCH and negative asymmetric values of TGARCH. From this, it can be inferred that good news has a greater impact on the volatility of index returns than bad news. The research results are crucial for investors, risk forecasters, and policy makers.

Oil price uncertainty and industrial production in oil-exporting countries

This study documents the interdependence of oil price volatility on industrial production of emerging oil-exporting economies - Brazil, Mexico and 35 OECD countries (as proxy for the world). We used the oil price of West Texas Intermediate (WTI) for the price of oil and industrial production indices for economic activity or real output. The study used dynamic conditional correlation – generalized autoregressive conditional heteroskedasticity (DCC-GARCH) and corrected, cDCC-GARCH models for symmetric estimation and employs GJR-GARCH for asymmetric estimation. Bry and Boschan (1971) monthly (BBM) nonparametric dating for peaks and troughs of business cycles were obtained for industrial production of the countries under study. Results from DCC and cDCC parameters reveal that the dynamic linkages between oil price and industrial production (IP) in Brazil in Brazil and Mexico persistently co-move and the interdependence between oil price and IP of the world is temporary. The symmetric and asymmetric estimation results show that past news and lagged volatility depict a significant influence on the current conditional volatility of the variables. The study also reports that the corrected cDCC-GARCH truly endorses DCC-GARCH estimates and further reveals that the GJR-GARCH asymmetric model outperforms the symmetric GARCH models. The study, therefore, recommends that Brazil and Mexico should diversify their economies and heavily venture into non-oil exports for alternate revenues.

Using Models of the GARCH Family to Estimate the Level of Food and Non-Food Inflation in Ethiopia

An increase in inflation volatility implies higher uncertainty about future prices. As a result, producers and consumers can be affected by the increased inflation volatility, because it increases the uncertainty and the risk in the market. Thus, inflation volatility attracts the attention of researchers to find a suitable model which can predict the future conditions of the market. This study aims to fit appropriate ARMA-GARCH family models for food and non-food inflation rate of from the period January 1971 through June 2020. Since the main objective of the study is identifying an appropriate model for inflation series, the null and alternative hypotheses are defined in comparison of the two types of models. H0: The symmetric GARCH models better capture inflation volatility of Ethiopia. H1: The asymmetric GARCH models better capture inflation volatility of Ethiopia. The ARMA-GARCH family models were applied to capture the stylized facts of financial time series such us leptokurtic, volatility clustering and leverage effects. The mean model results show that, an ARMA (1, 2) and ARIMA (0, 1, 1) models are identified as the best fitted model for food and non-food inflation, respectively. From the estimation results of volatility model, an asymmetric TGARCH (1, 1) model with Student's t- distributional assumptions of the residual is the best model for non-food inflation. Thus, modeling of information, news of events is very significant determinants of volatility and GARCH family models are appropriate for the given series (monthly food-inflation volatility) of Ethiopia under the study period considered.

India VIX and Forecasting Ability of Symmetric and Asymmetric GARCH Models

Volatility forecasting plays an important role in decisions concerning risk assessment, asset valuation and monetary policy formulation. Forecasting implied volatility is a key parameter in pricing of options. Thus, through this paper we attempt to model and test the predictive ability of symmetric GARCH(1,1) and asymmetric TGARCH(1,1) and EGARCH(1,1) models in forecasting the India Volatility Index (VIX). The estimated results confirm the dependency of volatility on its past behavior. It discloses that conditional variance takes longer to disintegrate and the innovations to it are highly persistent in nature. The predictive ability of these models to forecast the direction of the VIX series is evaluated by employing a standard (symmetric) loss function, such as the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE) and Theil’s inequality coefficient. The results show that the GARCH(1,1) provides superior forecasts compared to other models.

Does Trading Volume explain the Information Flow of Crude Palm Oil Futures Returns?

This study examines the role of trading volume in the crude palm oil (CPO)futures market as a proxy for information áow from the perspective of the mixture-of-distributions hypothesis (MDH). Using the data from January 2000 to April 2017, a sym-metric GARCH model has been estimated, in which the residuals follow alternatively thenormal Student-t and generalised error distribution. An alternative augmented model thatconsists of trading volume as an exogenous variable is estimated with the same error dis-tributions. Our results suggest several conclusions: First, the trading volume could not actas a true proxy for information áow. This indicates that volume of futures trading containsrelatively less price-sensitive information. Secondly, the inclusion of trading volume into theconditional variance equation with Student-t distributed errors is important for modellingpurposes when the returns are leptokurtic and positively skewed. Hence, it can be concludedthat the use of return and trading volume will enhance the current information set usedby practitioners and analysts in pricing the CPO futures contract when there exists a highdegree of leptokurtosis in the returns. This is the Örst study that validates the MDH in thecontext of the CPO futures market

INVESTIGATING ABNORMAL VOLATILITY TRANSMISSION PATTERNS BETWEEN EMERGING AND DEVELOPED STOCK MARKETS: A CASE STUDY

The main aim of this paper is to investigate volatility spillover effects, the impact of past volatility on present market movements, the reaction to positive and negative news, among selected financial markets. The sample stock markets are geographically dispersed on different continents, respectively North America, Europe and Asia. We also investigate whether selected emerging stock markets capture the volatility patterns of developed stock markets located in the same region. The empirical analysis is focused on seven developed stock market indices, i.e. IBEX35 (Spain), DJIA (USA), FTSE100 (UK), TSX Composite (Canada), NIKKEI225 (Japan), DAX (Germany), CAC40 (France) and five emerging stock market indices, i.e. BET (Romania), WIG20 (Poland), BSE (India), SSE Composite (China) and BUX (Hungary) from January 2000 to June 2018. The econometric framework includes symmetric and asymmetric GARCH models i.e. EGARCH and GJR which are performed in order to capture asymmetric volatility clustering, interdependence, correlations, financial integration and leptokurtosis. Symmetric and asymmetric GARCH models revealed that all selected financial markets are highly volatile, including the presence of leverage effect. The stock markets in Hungary, USA, Germany, India and Canada exhibit high positive volatility after global financial crisis.

Asymmetric volatility spillovers between world oil prices and stock markets of the G7 countries in the presence of structural breaks

AbstractThe purpose of this paper is to examine the volatility transmission between oil prices and the seven major stock markets (G7) using symmetric and asymmetric bivariate GARCH models incorporating structural breaks. Since these countries play a crucial role in the international economy, it is important for financial market participants to understand the volatility transmission process for designing optimal portfolio allocations. We examine weekly data over the period 1998–2017 and endogenously detect structural breaks in variance using an iterated algorithm in order to estimate the volatility dynamics with greater accuracy. The models were estimated using the maximum likelihood method, and the BFGS algorithm was employed to obtain the variance–covariance estimation and the corresponding standard errors. Overall, we find volatility spillovers between markets together with the fact that the oil market has a leading role. More importantly, we show that neglecting structural changes in variance and/or asymmetries may lead to biased volatility spillover effects. Furthermore, the results highlight that models ignoring structural breaks are significantly overestimating the effect of their own past volatility on the current volatility. In addition, we find that disregarding asymmetries could also lead to erroneous estimates of these effects. Finally, we compute dynamic risk‐minimizing hedge ratios and optimal portfolio weights, however, no significant discrepancies are found among the models considered.

Dynamics of Time Varying Volatility in Stock Returns: Evidence from Nepal Stock Exchange

This study examines the properties of time varying volatility of daily stock returns in Nepal over the period 2011-2020 using 2059 observations on daily returns of NEPSE index series. The study examines various symmetric and asymmetric GARCH family models using several specifications of error distribution. The results of symmetric GARCH (1,1) and GARCH-M (1, 1) models indicate that there is volatility persistence in daily returns on composite NEPSE index series over the sampled period. However, the estimated results for GARCH-M (1, 1) models show that the stock returns in Nepal offer no significant risk premium to hedge against risk associated with investment in stocks. The study also demonstrates that asymmetric TGARCH (1, 1) and EGARCH (1, 1) models fail to capture the leverage effects on the volatility. Finally, study results show that GARCH (1, 1) with student’s t error distribution model is the best fitted one to capture the volatility persistence of daily returns on NEPSE index series over the sampled period. The findings from this study offers an additional insight in understanding the volatility pattern of daily stock returns in Nepal for the most recent period that helps investors in forming a sound strategy to address the risk pattern of investing in stock market of Nepal.

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.

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.

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.

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.