GARCH Family Models Research Articles

A Theoretical Evaluation of the Models for Stock Market Volatility

Volatility forecasting has been widely debated in empirical finance, nevertheless, studies examining issues in volatility and their resolution through various models has received a scant attention. Therefore, the present study which is purely a review work aims to elucidate volatility stylised facts along with discussion on theoretical foundation and procedure of volatility forecasting approaches. To serve this purpose, about sixty research papers were reviewed to extract meaningful insights on stock market volatility and its measurement methods. As a whole, it is observed that unconditional models that are intuitive and simple in estimation ignore most of well-known ‘stylised facts’ about volatility. GARCH family models though cater to most of volatility stylised facts, yet at the practioners’ level, EWMA approach appears to be more reliable and worthwhile. Further, studies show that it is difficult to evaluate GARCH models as empirical results of such a model are dependent on the sampling frequency. Hence, choice among such models remains to be an empirical issue sensitive to length and frequency of data. Finally, GARCH family models expected to take care of main stylised facts like, volatility clustering, asymmetric effect, etc., yet models that have a capacity to handle properties like, non-normal behaviour of stock market volatility are beyond the purview of this study, thus represent a future gap for a literature review based research.

Forecasting the realized volatility of CSI 300

According to the characteristics of realized volatility existing in Shanghai and Shenzhen 300 index (China Securities Index 300, CSI 300), the GARCH family model is introduced to describe the ARCH effect of error sequences in HAR, ARFIMA, and ARFIMAX models. Then, the HAR-GARCH family, the ARFIMA-GARCH family, and the ARFIMAX-GARCH family models set is proposed, which contains 33 kinds of models. Using the quasi maximum likelihood method, the parameters of the all models are estimated with normal (N) and skewed student t (SKST) distributions. By rolling window technology, one-step-ahead rolling prediction of realized volatility for CSI 300 is conducted. The results from prediction accuracy by model confidence set (MCS) test show that the realized volatility prediction models with skewed student t distribution possess higher precision than those of normal distribution in general. The ARFIMAX and other six models in ARFIMAX-GARCH family form the optimal prediction models set, which can forecast the realized volatility of CSI 300 with better accuracy.

What Drives China's 2015 Stock Market Surges and Turmoil?

AbstractUsing high‐frequency data, we investigate China's stock market surges and turmoil from 2014 to 2015 by employing GARCH family models to evaluate the effects of government policies, economic factors, and related announcements. The results indicate that China's stock market has primarily been driven by government policies rather than economic factors. During the period, the commentaries of the People's Daily further amplified the direction of market movements in the market surges and turmoil. In addition to individual policies and announcements, we explore the structural changes in volatility in different market stages and provide explanations for the distinct features of each stage.

A Comparison of GARCH Type Models With the SV Model on the Financial Markets of BRICS

We examine the effectiveness of GARCH models and the SV model in foreign exchange rates and the stock indices of the BRICS. The empirical analysis is conducted using the daily log returns. The data cover the period 13/05/1999-22/11/2018. The theoretical results are confirmed by running the models with the use of R programming language. The conditional variance is modelled with a GARCH (1,1), IGARCH, EGARCH,GJR-GARCH and the Standard Stochastic Volatility model (SV) model. The results suggest that the GJR model outperforms the other GARCH-family models and provides a clear direction on how to critically estimate volatility and infer conclusions. The SV model provides better forecasting results from the standardized GARCH(1,1). The forecasting power of EGARCH performs better, as it indicates lower values in the loss functions After the forecasting tools for evaluation the forecasting results are used. These are the Root Mean Squared Error (RMSE),the Mean Squared Error (MSE) the Mean Absolute Error (MAE). Our findings strongly suggest that more research should be conducted by using different distributions to get more accurate results. Therefore we suggest that the asset returns of sectors and their independent relations, as it would be very helpful for policy practitioners.

Modeling exchange rate return volatility of RMB/USD using GARCH family models

ABSTRACT The paper examines volatility of RMB exchange rate return of onshore and offshore markets. The onshore rate covered 4/01/2008–5/09/2016 while offshore spanned 31/12/2008-22/09/2016, the returns were not normally distributed and were integrated of order zero I(0). The Ljung-Box Q statistics depicts the presence of autocorrelation in return series and Ljung-Box Q2 statistics of power transformed for conditional heteroscedasticity for lags of 6, 12 and 20 all indicated the presence of conditional heteroscedascity. The exchange rates volatility was persistent in both markets. However, offshore return was more persistent while leverage effects exist in both markets. Asymmetry power Autoregressive conditional Heteroscedastic (APARCH) model was the best model for forecasting purposes in both markets while Glosten, Jogannathan and Rankle, Generalized Autoregressive conditional Heteroscedastic (GJR-GARCH) model and Integrated Generalized Autoregressive conditional Heteroscedastic (I-GARCH) were the worst models in onshore and offshore return markets respectively. APARCH model should be adopted for future studies.

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.

Forecasting the Volatility of Stock Market Index Using the Hybrid Models with Google Domestic Trends

In order to improve the forecasting accuracy of the volatilities of the markets, we propose the hybrid models based on artificial neural networks with multi-hidden layers in this paper. Specifically, the hybrid models are built using the estimated volatilities obtained from GARCH family models and Google domestic trends (GDTs) as input variables. We further carry out many experiments varying the number of layers and activation functions to obtain the accurate hybrid model for forecasting volatility. The proposed models are applied to forecast weekly and monthly volatilities of S&P 500 index to verify their accuracy. The performance comparison results show that the hybrid models with GDTs outperform clearly the predicted results with GARCH family models and the hybrid models without GDTs in forecasting the volatility of actual market. We also provide the experiment results with graphs to illustrate the efficiency of models.

Half-Life Volatility Measure of the Returns of Some Cryptocurrencies

This paper explores the half-life volatility measure of three cryptocurrencies (Bitcoin, Litecoin and Ripple). Two GARCH family models were used (PGARCH (1, 1) and GARCH (1, 1)) with the student-t distribution. It was realised that, the PGARCH (1, 1) was the most appropriate model. Therefore, it was used in determining the half-life of the three returns series. The results revealed that, the half-life was 3 days, 6 days and 4 days for Bitcoin, Litecoin and Ripple respectively. This shows that, the three coins have strong mean reversion and short half-life and that it takes the respective days for volatility in each of coin to return half way back without further volatility.

Volatility Analysis of Commodity Futures and Common Stocks Market: An Example of India

The paper investigates the pattern of volatility in daily return from select Commodity Futures and Stock market in India. One Commodity Future from each group of futures is chosen for the study and they are-Potato, Gold, Crude oil and Mentha Oil. S&P CNX Nifty is selected as a representative of stock market. This study uses several econometrics techniques and in particular, GARCH family models are used for examining the volatility aspects of commodity futures and Nifty Index. The results obtained point to the fact that Crude Oil and Gold futures market is almost similar to the functioning of the stock market in India.

Crypto-currencies, Fiat Money or Gold Standard; An Empirical Evidence from Volatility Structure Analysis Using News Impact Curve

This study investigates whether symmetric and asymmetric volatility effects are persisted in the daily return series of Bitcoin currency compared to the gold and fiat money system using GARCH family models. The symmetric analysis shows that the three monetary systems exhibit time-varying volatility with high persistence and predictability behaviour whereas asymmetric analysis indicates that Bitcoin currency and gold are not significantly respond to asymmetric information effects in the financial markets however, the US dollar index is affected by the positive shocks. This suggesting Bitcoin and gold have the capability for hedging or safe-haven assets against market risk specifically during times of economic turmoil. Evidence suggests that cryptocurrency is a potential alternative to current fiat money system, offering benefit for policy makers and a good investment option for positional investors in terms of hedging, portfolio diversification strategy and risk management.

The Influences of Book-to-Price Ratio and Stock Capitalization on Value-at-Risk Estimation in Taiwan Stock Market

ABSTRACTThis study examines whether the stock capitalization and book-to-price (B/P) ratio can affect the VaR (value-at-risk) estimation performances in six VaR estimation methodologies. Examining on the daily returns on Taiwan stock market, we find that the market capitalization is not a significant factor in VaR estimation, while the B/P ratio is generally positively related to VaR estimates. Among various VaR estimation models, the historical simulation model performs the best, and the followers are the Student-t and extreme value theory models. Reversely, normal distribution model performs the worst, and the GARCH-family models frequently extremely over-estimate or under-estimate the individual daily VaR.

Modeling and Forecasting Market Value-at-Risk of DS30 Index through GARCH Family Models with Heavy Tail Distribution

Modeling and Forecasting Market Value-at-Risk of DS30 Index through GARCH Family Models with Heavy Tail Distribution

Implied Volatility across Geographical Markets and Asset Classes

Derivatives based on the VIX index and related indexes in the U.S. and around the world have proliferated enormously in the last few years. This article reviews the behavior of VIX-like indexes in 14 markets in 8 countries. Eleven are stock indexes, 2 are commodities, and the last is the USD–EUR exchange rate. A simple GARCH-family model for the change and volatility of the index is fitted to index returns, implied volatility (i.e., lagged IV), and the U.S. VIX (as a proxy for global volatility conditions). Separate coefficients are estimated for positive and negative variable values, which reveals that negative market returns cause sharp and immediate increases in the volatility index, but positive returns reduce implied volatility by a lesser amount and the effect is spread out over time. Including lagged factors from the previous day was important, especially for the smaller markets. The U.S. VIX was found to influence all of the other markets, thus suggesting the existence of a global volatility factor that can be proxied by the VIX, and the evidence indicates that volatility appears to spill over from the first-tier markets to the smaller ones.

Dynamic jumps in global oil price and its impacts on China's bulk commodities

This paper investigated the impacts of oil price shocks, especially dynamic jumps in its returns on China's bulk commodity markets at both the aggregate and industry levels. After setting a zero lower bound to the jump intensity of the ARJI model, we found that dynamic jumps exist in oil price movements. Moreover, under shocks of oil price jumps, not only the returns but also the risks of China's bulk commodity markets are affected significantly, and the reactions of risks are characterized by “overreactions”. Meanwhile, by decomposing oil price shocks into expected positive (negative), and unexpected positive (negative) components, we discovered that the impacts of unexpected shocks are positive and significantly asymmetric at both levels, while those of the expected shocks are negative and insignificantly asymmetric at the industry level. In addition, the volatility clustering of all price movements and the permanent volatility effects on China's bulk commodities are also authenticated by applying the GARCH family models.

Conditional volatility nexus between stock markets and macroeconomic variables

PurposeThe purpose of this paper is to analyse the relation between stock market volatility and macroeconomic fundamentals for G-7 countries using monthly data over the period from July 1985 to June 2015.Design/methodology/approachThe empirical methodology is based on two steps: in the first step, the authors obtain the conditional volatilities of stock market returns and macroeconomic variables through the GARCH family of models. The authors also incorporate the impact of early 2000s dotcom and the global financial crises. In the second step, the authors estimate multivariate vector autoregressive model to analyze the dynamic relation between stock markets return and macroeconomic variables.FindingsThe overall results for G-7 countries indicate a weak volatility transmission from macroeconomic factors to stock market volatility at individual level but the collective impact of volatility transmission is highly significant. Although, the results of block exogeneity indicate a bidirectional causality except UK, but the causal linkage is quite weak from stock market to macroeconomic variables. Moreover, the local financial variables excluding interest rate are closely integrated, and the volatility of industrial production growth and oil price are identified as the most significant macroeconomic factors that could possibly influence the directions of stock markets.Originality/valueThis research establishes the nature of the links between stock market and macroeconomic volatility. Research to date has been unable to satisfactorily establish the empirical nature of such links. The authors believe this paper begins to do this.

Forecasting crude oil price volatility in India using a hybrid ANN-GARCH model

In this paper the volatility forecasts of crude oil commodity price returns are analysed. Various GARCH family models are used to forecast the volatility and the output in terms of return vectors of these models are used as inputs for a neural network. The return forecasting performance of the GARCH family models are compared with GARCH-ANN models using root mean square error as the criteria. The results show that the hybrid model of ANN and EGARCH gives the best performance. An explanatory variable, the exchange rate between Indian Rupee and Saudi Arabia Riyal is used as input for the neural network model for the second scenario and using the same criteria of root mean square error, it is observed to have no improvement over the previous ANN-GARCH models.

Measuring Risk and Leverage Patterns of Indian and Chinese Stock Markets: Evidence from Pre and Post Global Financial Crisis

To understand the nature of stock markets is important in investment opportunities. The study focusses on the risk and leverage pattern of stock markets taking India and China as a sample by using daily data of CNX Nifty and Shanghai from 1992 to 2015. By accounting the structural break of GFC (Global Financial Crisis), the data was split in two parts, i.e., pre and post global financial crisis. The study applied GARCH family models to capture the results indicating highly significant ARCH and GARCH parameters for both Indian and Chinese markets for pre and post-crisis period and there was also an evidence of GARCH in Mean model effect in Shanghai market during the Pre-crisis period. The results of the asymmetric model shows that good news creates less volatility than bad news for all the periods except for Shanghai Composite Index in post-crisis which shows negative and insignificant effect.

The best of two worlds: Forecasting high frequency volatility for cryptocurrencies and traditional currencies with Support Vector Regression

This paper provides an evaluation of the predictive performance of the volatility of three cryptocurrencies and three currencies with recognized stores of value using daily and hourly frequency data. We combined the traditional GARCH model with the machine learning approach to volatility estimation, estimating the mean and volatility equations using Support Vector Regression (SVR) and comparing to GARCH family models. Furthermore, the models’ predictive ability was evaluated using Diebold-Mariano test and Hansen’s Model Confidence Set. The analysis was reiterated for both low and high frequency data. Results showed that SVR-GARCH models managed to outperform GARCH, EGARCH and GJR-GARCH models with Normal, Student’s t and Skewed Student’s t distributions. For all variables and both time frequencies, the SVR-GARCH model exhibited statistical significance towards its superiority over GARCH and its extensions.

Forecasting stock market volatility and information content of implied volatility index

ABSTRACTThis study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.

Information demand and stock return predictability

Recent theoretical work suggests that signs of asset returns are predictable given that their volatilities are. This paper investigates this conjecture using information demand, approximated by the daily internet search volume index (SVI) from Google. Our results reveal that incorporating the SVI variable in various GARCH family models significantly improves volatility forecasts. Moreover, we demonstrate that the sign of stock returns is predictable contrary to the levels, where predictability has proven elusive in the US context. Finally, we provide novel evidence on the economic value of sign predictability and show that investors can form profitable investment strategies using the SVI.