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A Hybrid Fuzzy GJR-GARCH Modeling Approach for Stock Market Volatility Forecasting  [cached]
Leandro Maciel
Revista Brasileira de Finan?as , 2012,
Abstract: Forecasting stock market returns volatility is a challenging task that has attracted the attention of market practitioners, regulators and academics in recent years. This paper proposes a Fuzzy GJR-GARCH model to forecast the volatility of S&P 500 and Ibovespa indexes. The model comprises both the concept of fuzzy inference systems and GJR-GARCH modeling approach in order to consider the principles of time-varying volatility, leverage effects and volatility clustering, in which changes are cataloged by similarity. Moreover, a differential evolution (DE) algorithm is suggested to solve the problem of Fuzzy GJR-GARCH parameters estimation. The results indicate that the proposed method offers significant improvements in volatility forecasting performance in comparison with GARCH-type models and with a current Fuzzy-GARCH model reported in the literature. Furthermore, the DE-based algorithm aims to achieve an optimal solution with a rapid convergence rate.
Testing and Predicting Volatility Spillover—A Multivariate GJR-GARCH Approach  [PDF]
Hira Aftab, Rabiul Alam Beg, Sizhong Sun, Zhangyue Zhou
Theoretical Economics Letters (TEL) , 2019, DOI: 10.4236/tel.2019.91008

This paper proposes a multivariate VAR-BEKK-GJR-GARCH volatility model to assess the dynamic interdependence among stock, bond and money market returns and volatility of returns. The proposed model allows for market interaction which provides useful information for pricing securities, measuring value-at-risk (VaR), and asset allocation and diversification, assisting financial regulators for policy implementation. The model is estimated by the maximum likelihood method with Student-t innovation density. The asymptotic chi-square tests for volatility spillovers and leverage effects are constructed and provide predictions of volatility and time-varying correlations of returns. Application of the proposed model to the Australia’s domestic stock, bond, and money markets reveals that the domestic financial markets are interdependent and volatility is predictable. In general, volatility spillovers from stock market to bond and to money markets due to common news. The empirical findings of this paper quantify the association among the security markets which can be utilized for improving agents’ decision-making strategies for risk management, portfolio selection and diversification.

Forecasting crude oil market volatility: can the Regime Switching GARCH model beat the single-regime GARCH models?  [PDF]
Yue-Jun Zhang,Ting Yao,Ling-Yun He
Quantitative Finance , 2015,
Abstract: In order to obtain a reasonable and reliable forecast method for crude oil price volatility, this paper evaluates the forecast performance of single-regime GARCH models (including the standard linear GARCH model and the nonlinear GJR-GARCH and EGARCH models) and the two-regime Markov Regime Switching GARCH (MRS-GARCH) model for crude oil price volatility at different data frequencies and time horizons. The results indicate that, first, the two-regime MRS-GARCH model beats other three single-regime GARCH type models in in-sample data estimation under most evaluation criteria, although it appears inferior under a few of other evaluation criteria. Second, the two-regime MRS-GARCH model overall provides more accurate volatility forecast for daily data but this superiority dies way for weekly and monthly data. Third, among the three single-regime GARCH type models, the volatility forecast of the nonlinear GARCH models exhibit greater accuracy than the linear GARCH model for daily data at longer time horizons. Finally, the linear single-regime GARCH model overall performs better than other three nonlinear GARCH type models in Value-at-Risk (VaR) forecast.
Modeling Exchange Rate Volatility: Application of the GARCH and EGARCH Models  [PDF]
Manamba Epaphra
Journal of Mathematical Finance (JMF) , 2017, DOI: 10.4236/jmf.2017.71007
Abstract: Policy makers need accurate forecasts about future values of exchange rates. This is due to the fact that exchange rate volatility is a useful measure of uncertainty about the economic environment of a country. This paper applies univariate nonlinear time series analysis to the daily (TZS/USD) exchange rate data spanning from January 4, 2009 to July 27, 2015 to examine the behavior of exchange rate in Tanzania. To capture the symmetry effect in exchange rate data, the paper applies both ARCH and GARCH models. Also, the paper employs exponential GARCH (EGARCH) model to capture the asymmetry in volatility clustering and the leverage effect in exchange rate. The paper reveals that exchange rate series exhibits the empirical regularities such as clustering volatility, nonstationarity, non-normality and serial correlation that justify the application of the ARCH methodology. The results also suggest that exchange rate behavior is generally influenced by previous information about exchange rate. This also implies that previous day’s volatility in exchange rate can affect current volatility of exchange rate. In addition, the estimate for asymmetric volatility suggests that positive shocks imply a higher next period conditional variance than negative shocks of the same sign. The main policy implication of these results is that since exchange rate volatility (exchange-rate risk) may increase transaction costs and reduce the gains to international trade, knowledge of exchange rate volatility estimation and forecasting is important for asset pricing and risk management.
Modeling and Forecasting Stock Market Volatility by Gaussian Processes based on GARCH, EGARCH and GJR Models  [PDF]
PhichHang Ou,Hengshan Wang
Lecture Notes in Engineering and Computer Science , 2011,
Implementation of the Estimating Functions Approach in Asset Returns Volatility Forecasting Using First Order Asymmetric GARCH Models  [PDF]
Timothy Ndonye Mutunga, Ali Salim Islam, Luke Akong’o Orawo
Open Journal of Statistics (OJS) , 2015, DOI: 10.4236/ojs.2015.55047
Abstract: This paper implements the method of estimating functions (EF) in the modelling and forecasting of financial returns volatility. This estimation approach incorporates higher order moments which are common in most financial time series, into modelling, leading to a substantial gain of information and overall efficiency benefits. The two models considered in this paper provide a better in-sample-fit under the estimating functions approach relative to the traditional maximum likely-hood estimation (MLE) approach when fitted to empirical time series. On this ground, the EF approach is employed in the first order EGARCH and GJR-GARCH models to forecast the volatility of two market indices from the USA and Japanese stock markets. The loss functions, mean square error (MSE) and mean absolute error (MAE), have been utilized in evaluating the predictive ability of the EGARCH vis-à-vis the GJR-GARCH model.
An Empirical Evaluation in GARCH Volatility Modeling: Evidence from the Stockholm Stock Exchange  [PDF]
Chaido Dritsaki
Journal of Mathematical Finance (JMF) , 2017, DOI: 10.4236/jmf.2017.72020
Abstract: In this paper, we use daily stock returns from the Stockholm Stock Exchange in order to examine their volatility. For this reason, we estimate not only GARCH (1,1) symmetric model but also asymmetric models EGARCH (1,1) and GJR-GARCH (1,1) with different residual distributions. The parameters of the volatility models are estimated with the Maximum Likelihood (ML) using the Marquardt algorithm (Marquardt [1]). The findings reveal that negative shocks have a large impact than positive shocks in this market. Also, indices for the return of forecasting have shown that the ARIMA (0,0,1)-EGARCH (1,1) model with t-student provide more precise forecasting on volatilities and expected returns of the Stockholm Stock Exchange.
On Modeling the Volatility of Nigerian Stock Returns Using GARCH Models  [cached]
C. E. Onwukwe,B. E. E. Bassey,I. O. Isaac
Journal of Mathematics Research , 2011, DOI: 10.5539/jmr.v3n4p31
Abstract: This study investigates the time series beaviour of daily stock returns of four firms listed in the Nigerian Stock Market from 2nd January, 2002 to 31st December, 2006, using three different models of heteroscedastic processes, namely: GARCH (1,1), EGARCH (1,1) and GJR-GARCH models respectively. The four firms whose share prices were used in this analysis are UBA, Unilever, Guiness and Mobil. All the return series exhibit leverage effect, leptokurtosis, volatility clustering and negative skewness, which are common to most economic financial time series. Except for Guiness, other series display significant level of second-order autocorrelation, satisfying covariance-stationary condition. These models were estimated assuming a Gaussian distribution using Brendt-Hall-Hall-Hausman (BHHH) algorithm's program in Eview software platform. The estimation results reveal that the GJR-GARCH (1, 1) gives better fit to the data and are found to be superior both in-sample and out-sample forecasts evaluation.
GARCH-Type Model with Continuous and Jump Variation for Stock Volatility and Its Empirical Study in China  [PDF]
Huannan Zhang,Qiujun Lan
Mathematical Problems in Engineering , 2014, DOI: 10.1155/2014/386721
Abstract: On the basis of GARCH-RV-type model, we decomposed the realized volatility into continuous sample path variation and discontinuous jump variation, then proposed a new volatility model which we call the GARCH-type model with continuous and jump variation (GARCH-CJ-type model). By using the 5-minute high frequency data of HUSHEN 300 index in China, we estimated parameters of the GARCH-type model, the GARCH-RV-type model, and the GARCH-CJ-type model and compared the three types of models’ predictive power to the future volatility. The results show that the realized volatility and the continuous sample path variation have certain predictive power for future volatility, but the discontinuous jump variation does not have that kind of function. What is more, the GARCH-CJ-type model has a more power to predict the future volatility than the other two types of models. Therefore, the GARCH-CJ-type model is much more useful for the research on the capital assets pricing, the derivative security valuation, and so on. 1. Introduction The research on asset volatility in financial market is the foundation of finance, such as capital assets pricing, financial derivatives pricing, and financial risk measurement. The premise of quantitative financial analysis is to accurately measure and predict asset volatility. Therefore, the measurement and prediction of asset volatility are a hotspot of research all the time. To measure and predict asset volatility accurately, Engle [1], in view of “clustering” and “persistence” of volatility, proposed an autoregressive conditional heteroscedastic (ARCH) model; Bollerslev [2] built a generalized ARCH (GARCH) model based on the ARCH model. Then, GARCH model was extended; Nelson [3] found that the asset volatility is “asymmetric.” He modified the GARCH model and built an EGARCH model; Glosten et al. [4] also examined the “asymmetry” and built a TGARCH model (also called GJR model). The above models (called GARCH-style model in this paper) have been proved to have strong power to predict the future volatility of assets [5]. Admittedly, GARCH-type models have fairly strong predictive power, but there is room for improvement, as the accuracy pursuit for future volatility prediction is endless in financial operations, such as financial asset pricing, financial derivative pricing, and financial risk management. Therefore, it is necessary to improve the predictive power of the models. In order to perfect the accuracy of predictions, the realized volatility (RV) as an exogenous variable has been introduced by Koopman et al. [6] into the
A Family of Stochastic Unit GARCH Models
Mamadou Abdoulaye Konte
International Journal of Economics and Finance , 2012, DOI: 10.5539/ijef.v5n1p177
Abstract: A class of Asymmetric GARCH models is presented. It shares the same unconditional variance and volatility forecast formula as the standard GARCH(P,Q) model under the assumption of a symmetric conditional distribution for innovations. use three models of this class to assess their ability to forecast S&P 500 market volatility and to make better decisions for the purpose of risk management and investment. Subsequently, a comparison is made with respect to competing models (GARCH, EGARCH, GJR). It was found that for the in-sample evaluation, the best model is obtained from the Stochastic Unit GARCH (SUGARCH) model where leverage effects are introduced through the GARCH (i.e) parameter. For the out-of-sample evaluation (QLIKE loss function), it is better to use the SUGARCH class where the asymmetry appears on the ARCH (i.e ) parameter.
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