Volatility Modeling and Forecasting Using Range-Based GARCH Models
Keywords:
Volatility, Conditional Variance, Range-based GARCH, Leptokurtic Distribution, Loss Function, Forecast Horizon
Abstract
This paper investigates the forecast performance of symmetric and asymmetric GARCH models in comparison with symmetric and asymmetric range-based GARCH models. Specifically, we explore whether including the range and assuming asymmetry in the conditional variance equation significantly impacts the forecast performance of range-based GARCH models. The models examined in this study include GARCH(1,1), TARCH(1,1), RGARCH(1,1,1), and RTARCH(1,1,1). Our evaluation of these models utilizes different loss functions.Using daily, weekly and monthly opening, closing, highest and lowest all-share historical prices of the Nigeria Stock Exchange from 2014 to 2024, the results of data analysis reveal that incorporating the range and accounting for asymmetry in the conditional variance equation enhances the forecast performance of range-based GARCH models. Importantly, this finding holds for daily, weekly, and monthly forecast horizons.
References
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[27] Padmakumari, L., and Shaik, M. (2023). An Empirical Investigation of Value at Risk (VaR) Forecasting Based on Range-Based Conditional Volatility Models. Engineering Economics, 34(3):275-292.
[28] Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics. 31, 307-327.
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[30] Engle, R. F. and Ng, V. K. (1993). Measuring and Testing The Impact of News on Volatility. The Journal of Finance, 48(5):1749-1778.
[31] Zakoian J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5):931–955.
[32] Bollerslev, T., Engle, R.F. and Nelson, D. (1994). ARCH models. Handbook of Econometrics, 4, 2959-3038.
[33] Hansen, P.R. and Lunde, A. A. (2005). Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1). Journal of Applied Econometric, 20(7):873–889.
[34] Anderson, T.G. and Bollerslev, T. (1998). Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts, International Economic Review, 39(4):885-905
[2] Garman, M. B., and Klass, M. J. (1980). On The Estimation of Security Price Volatilities from Historical Data. The Journal of Business, 53, 67-78.
[3] Ball, C. A., and Torous, W. N. (1984) The Maximum Likelihood Estimation of Security Price Volatility:Theory Evidence, and Application to Option Pricing. Journal of Business, 57(1):97- 112.
[4] Alizadeh, S., Brandt, M. and Diebold, F. X. (2002). Range-Based Estimation of Stochastic Volatility Models, Journal of Finance, 57, 1047-1092.
[5] Brandt, M. and Jones, C. S. (2006). Volatility Forecasting With Range-Based EGARCH Models. Journal of Business and Economic Statistics. Vol.24,No.4, 470-486.
[6] Shaik, M., and Maheswaran, S. (2016). Modelling The Paradox in Stock Markets by Variance Ratio Volatility Estimator That Utilises Extreme Values of Asset Prices. Journal of Engineering Market Finance, 15(3):333-361.
[7] Padmakumari, L., and Maheswaran, S. (2017). A New Statistic to Capture The Level Dependence in Stock Price Volatility. The Quarterly Review of Economics and Finance, 65, 355-362.
[8] Shaik, M., and Maheswaran, S. (2018). Expected Lifetime Range Ratio to Find Mean Reversion: Evidence From Indian Stock Market. Cogent Economics & Finance, 6(1):1475926.
[9] Shaik, M., and Maheswaran, S. (2019). Volatility Behavior of Asset Returns Based on Robust Volatility Ratio: Empirical Analysis on Global Stock Indices. Cogent Economics & Finance, 7(1):1597430
[10] Nieto, M. R., and Ruiz, E. (2016). Frontiers in VaR Forecasting and Backesting. International Journal of Forecasting, 32(2):475-501.
[11] Ma, F., Li, Y., Liu, L., and Zhang, Y. (2018). Are Low-Frequency Data Really Uninformative? A Forecasting Combination Perspective. The North American Journal of Economics and Finance, 44, 92-108.
[12] Onyeka-Ubaka, J.N.and Abass,O. (2018). On Optimal Estimate Functions for Asymmetric GARCH Models.International Journal of Mathematical Analysis and Optimization Theory and Applications. 2018, 291-311.
[13] Tabasi, H., Yousefi, V., Jamosaitiene, J., and Ghasemi, F. (2019). Estimating Conditional Value at Risk in The Tehran Stock Exchange Based on The Extreme Value Theory Using GARCH Models. Administrative Sciences, 9(2):40-56.
[14] Altun, E., Tathdil, H., and Ozel, G. (2019). Conditional ASGT-GARCH Approach to Valueat-Risk. Iranian Journal of Science and Technology, Transactions A: Science, 43(1):239-247.
[15] Milosevic, M., Andelic, G., Vidakovic, S., and Dakovic, V. (2019). The Influence of Holiday Effect on The Rate of Return of Emerging Markets: A Case Study of Slovenia, Croatia and Hungary. Economic Research-Ekonomska Isttrazivanja, 32(1):2354-2376.
[16] Faldzinski, M., Fiszeder, P., and Orzeszko, W. (2020). Forecasting Volatility of Energy Commodities: Comparison of GARCH Models With Support Vector Regression. Energies, 14(1):6. https://doi.org/10.3390/en14010006.
[17] Shaik, M., and Maheswaran, S. (2020). A New Unbiased Additive Robust Volatility Estimation Using Extreme Values of Asset Prices. Financial Markets and Portfolio Management, 34, 313- 347
[18] Aliyev, F., Ajayi, R., and Gasim, N. (2020). Modelling Asymmetric Market Volatility With Univariate GARCH Models: Evidence from Nasdaq-100. The Journal of Economic Asymmetries, 22, e00167.
[19] Onyeka-Ubaka,J.N., and Anene, U.J. (2020). Some Forecast Asymmetric GARCH Models for Distributions with Heavy Tails. International Journal of Mathematical Analysis and Optimization:Theory and Applications, 2020(1):689-706.
[20] Kim, J. M., Kim, D. H., and Jung, H. (2021). Estimating yield spreads volatility using GARCHtype models. The North American Journal of Economics and Finance, 57, 101396.
[21] Emenogu, N. G., and Adenomon, M. O. (2018). The Effect of High Positive Autocorrelation on the Performance of GARCH Family Models. DOI:10.20944/preprints201811.0381.v1
[22] Slim, S., Koubaa, Y., and BenSaida, A. (2017). Value-at-Risk Under Levy GARCH Models: Evidence from Global Stock Markets. Journal of International Financial Markets, Institutions and Money, 46, 30-53.
[23] Elenjical, t., Mwangi, P., Panulo, B., and Huang, C. S.(2016). A Comparative Cross-Regime Analysis on the Performance of GARCH-Based Value-at-Risk Models: Evidence from The Johannesburg Stock Exchange. Risk Management. 18, 89-110.
[24] Hongwiengjan, W., and Thongtha, D. (2021). An Analytical Approximation of Option Prices via TGARCH Model. Economic Research-Ekonomska Istrazivanja, 34(1):948-969.
[25] Baum, C. F., and Hurn, S. (2021). What Good is a Volatility Model: A Re-examination After 20 Years. Stata Journal: Promoting Communications on Statistics and Stata, 21(2):295-319.
[26] Naresh, C., Kummeta, R. S., and Ramanjaneyulu, N. (2023). Measuring Asymmetric Volatility of Bank Nifty Index Using EGARCH Model & Obstacle. Indian Journal of Economic and Finance (IJEF), 3(2):67-72.
[27] Padmakumari, L., and Shaik, M. (2023). An Empirical Investigation of Value at Risk (VaR) Forecasting Based on Range-Based Conditional Volatility Models. Engineering Economics, 34(3):275-292.
[28] Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics. 31, 307-327.
[29] Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of U.K. Inflation. Econometrica: Journal of the Econometric Society, 50, 987-1008.
[30] Engle, R. F. and Ng, V. K. (1993). Measuring and Testing The Impact of News on Volatility. The Journal of Finance, 48(5):1749-1778.
[31] Zakoian J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5):931–955.
[32] Bollerslev, T., Engle, R.F. and Nelson, D. (1994). ARCH models. Handbook of Econometrics, 4, 2959-3038.
[33] Hansen, P.R. and Lunde, A. A. (2005). Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1). Journal of Applied Econometric, 20(7):873–889.
[34] Anderson, T.G. and Bollerslev, T. (1998). Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts, International Economic Review, 39(4):885-905
Published
2024-10-30
How to Cite
Ogunwole , B. A., & Agunloye , O. K. (2024). Volatility Modeling and Forecasting Using Range-Based GARCH Models. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(4), 35 - 44. Retrieved from http://ijmso.unilag.edu.ng/article/view/2387
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