Volatility of pakistan stock market: A comparison of Garch type models with five distribution
Keywords:
Volatility, stock market, GARCH model, investor, economic
Abstract
This study conducts empirical analyses modeling the volatility of Pakistani stock market over the period of 1st January 2008 to 30th June 2018 via different GARCH type Model; Symmetric (GARCH & GARCH-M) and Asymmetric (EGARCH & TGARCH) with five different Distribution Techniques such as Normal Distribution (Norm), Student’s t Distribution (Std.), Generalized Error Distribution (GED), Student’s t Distribution with fix the degree of freedom (Std. with fix DOF) and Generalized Error Distribution with fix parameters (GED with fix parameters). The results are shown in GARCH (1, 1) lagged conditional variance and squared disturbance which effects conditional variance is significant in all distribution. GARCH-M (1, 1) depicts a positive significant at 1% results in Std. and GED which indicates the existence of risk premium and insignificant in rest of the distribution on. EGARCH and TGARCH both are found to leverage effect significant at 1% level. In determining the accuracy and adequacy of forecasting density and choice of volatility model the results on simulated data indicates choice of conditional distribution appear as a more dominant factor. EGARCH model with Student’s t the distribution technique is delivered satisfactory results as compare to other models which censored by statistical tools of maximum Log Likelihood, minimum AIC, and SIC. The previous study of Pakistani Stock Market is limited to GARCH family models with one or two distributions. This study covers the limitations and also contributes existing literature in this regard. This research is considered important for investors, policymakers, and researchers.
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References
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Alberg, D., Shalit, H., & Yosef, R. (2008). Estimating stock market volatility using asymmetric GARCH models. Applied Financial Economics, 18(15), 1201-1208.
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Asemota, O. J., & Ekejiuba, U. C. (2017). An Application of Asymmetric GARCH Models on Volatility of Banks Equity in Nigeria’s Stock Market. CBN Journal of Applied Statistics. 8 (1), 73-99.
Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian journal of statistics, 171-178.
Banumathy, K., & Azhagaiah, R. (2015). Modelling Stock Market Volatility: Evidence from India. Managing Global Transitions: International Research Journal, 13(1), 28-42.
Black, F. (1976). Studies of stock price volatility of changes. American Statistical Association Journal. 177-181.
Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345-370.
Bucevska, V. (2013). An Empirical evaluation of GARCH models in value-at-risk estimation: Evidence from the Macedonian stock exchange. Business systems research journal: international journal of the Society for Advancing Business & Information Technology (BIT), 4(1), 49-64.
Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological methods & research, 33(2), 261-304.
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Ding, Z., Granger, C. W., & Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of empirical finance, 1(1), 83-106.
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 50 (4), 987-1007.
Engle, R. F., & Bollerslev, T. (1986). Modelling the persistence of conditional variances. Econometric reviews, 5(1), 1-50.
Engle, R. F., & Ng, V. K. (1993). Measuring and testing the impact of news on volatility. The journal of finance, 48(5), 1749-1778.
Engle, R. F., Lilien, D. M., & Robins, R. P. (1987). Estimating time varying risk premia in the term structure: The ARCH-M model. Econometrica: journal of the Econometric Society, 391-407.
Fang, J., Nakamura, H., & Maeda, H. (2011). The EPR effect: unique features of tumor blood vessels for drug delivery, factors involved, and limitations and augmentation of the effect. Advanced drug delivery reviews, 63(3), 136-151.
Fernández, C., & Steel, M. F. (1998). On Bayesian modeling of fat tails and skewness. Journal of the American Statistical Association, 93(441), 359-371.
Floros, C. (2008). Modelling volatility using GARCH models: evidence from Egypt and Israel. Middle Eastern Finance and Economics, (2), 31-41.
Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The journal of finance, 48(5), 1779-1801.
Gosset, W. S. (1908). Probable error of a correlation coefficient. Biometrika, 6(2-3), 302-310.
Goudarzi, H., & Ramanarayanan, C. S. (2010). Modeling and estimation of volatility in the Indian stock market. International Journal of Business and Management, 5(2), 85.
Hameed, A., Ashraf, H., & Siddiqui, R. (2006). Stock Market Volatility and Weak-form Efficiency: Evidence from an Emerging Market [with Comments]. The Pakistan Development Review, 1029-1040.
Hannan, E. J., & Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society. Series B (Methodological), 190-195.
Hassan, H. E., Mercer, S. L., Cunningham, C. W., Coop, A., & Eddington, N. D. (2009). Evaluation of the P-glycoprotein (Abcb1) affinity status of a series of morphine analogs: comparative study with meperidine analogs to identify opioids with minimal P-glycoprotein interactions. International journal of pharmaceutics, 375(1-2), 48-54.
Higgins, M. L., & Bera, A. K. (1992). A class of nonlinear ARCH models. International Economic Review, 137-158.
Hung , N. T. (2018). An empirical analysis of Euro Hungarian Forint exchange rate volatility using GARCH. Challenges in National and International Economic Policies. 57–67.
Jarque, C. M., & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review/Revue Internationale de Statistique, 163-172.
Jyothi , U., & Suresh, K. (2014). Estimating Stock Market Volatility Using Non-linear Models . IOSR Journal of Business and Management (IOSR-JBM). 62-65.
Kanasro, H. A., Rohra, C. L., & Junejo, M. A. (2009). Measurement of stock market volatility through ARCH and GARCH models: a case study of Karachi stock exchange. Australian Journal of Basic and Applied Sciences, 3(4), 3123-3127.
Karmakar, M. (2005). Modeling conditional volatility of the Indian stock markets. Vikalpa, 30(3), 21-38.
Khan, N. (2011). Dividend policy and the stock market reaction to dividend announcements in Pakistan (Doctoral dissertation, University of Dundee).
Kumar , H. P., & Patil , B. S. (August 2016 ). Volatility Forecasting- A Performance Measure of GARCH Techniques with Different Distribution Models. International Journal of Soft Computing, Mathematics and Control (IJSCMC), 5(No), 1-13.
Lim, C. M., & Sek, S. K. (2013). Comparing the performances of GARCH-type models in capturing the stock market volatility in Malaysia. Procedia Economics and Finance, 5, 478-487.
Ling, S., & McAleer, M. (2003). Asymptotic theory for a vector ARMA-GARCH model. Econometric theory, 19(2), 280-310.
Mwita, P. N., & Nassiuma, D. K. (2015). Volatility estimation of stock prices using Garch method. Kabarak Journal of Research & Innovation, 3(1), 48-53.
Najjar, M., Saleh, D., Zelic, M., Nogusa, S., Shah, S., Tai, A., ... & Whalen, M. J. (2016). RIPK1 and RIPK3 kinases promote cell-death-independent inflammation by Toll-like receptor 4. Immunity, 45(1), 46-59.
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica: Journal of the Econometric Society, 347-370.
Olbrys, J. (2013). Price and volatility spillovers in the case of stock markets located in different time zones. Emerging Markets Finance and Trade, 49(sup2), 145-157.
Omorogbe, J. A., Mc Nally, M., Cretu, I., & O'Connor, A. (2017). Mo1181 Gastric Intestinal Metaplasia Outcomes: Results From a 17 Year Tertiary Centre Upper GI Surveillance Programme in Ireland. Gastrointestinal Endoscopy, 85(5), AB452-AB453.
Peters, J. P. (2001). Estimating and forecasting volatility of stock indices using asymmetric GARCH models and (Skewed) Student-t densities. Preprint, University of Liege, Belgium, 3, 19-34.
Poon, S. H., & Granger, C. W. (2003). Forecasting volatility in financial markets: A review. Journal of economic literature, 41(2), 478-539.
Saeed, A. F., Wang, R., Ling, S., & Wang, S. (2017). Antibody engineering for pursuing a healthier future. Frontiers in microbiology, 8, 495.
Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, 6(2), 461-464.
Shah, A., Shahf, A. H., Parveen, N., Rehman, Z. U., Khan, S. Z., Rana, U. A., ... & Qureshi, R. (2016). Synthesis and electrochemical investigations of piperazines. Electrochimica Acta, 220, 705-711.
Stoyanov, J. V., Gantenbein-Ritter, B., Bertolo, A., Aebli, N., Baur, M., Alini, M., & Grad, S. (2011). Role of hypoxia and growth and differentiation factor-5 on differentiation of human mesenchymal stem cells towards intervertebral nucleus pulposus-like cells. Eur Cell Mater, 21(533), e47.
Taylor, S. J. (2008). Modelling financial time series. world scientific.
Theodossiou, P. (1998). Financial data and the skewed generalized t distribution. Management Science, 44(12-part-1), 1650-1661.
Vijayalakshmi, S., & Gaur, S. (2013). Modelling volatility: Indian stock and foreign exchange markets. Journal of Emerging Issues in Economics, Finance and Banking, 2(1), 583-98.
Wennström, A. (2014). Volatility Forecasting Performance: Evaluation of GARCH type volatility models on Nordic equity indices.
Wilhelmsson, A. (2006). Garch Forecasting Performance under Different Distribution Assumptions. Journal of Forecasting, 25, 561–578.
Zakoian, J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and control, 18(5), 931-955.
Akaike, H. (1974). A new look at the statistical model identification. IEEE transactions on automatic control, 19(6), 716-723.
Akhtar, S., & Khan, N. (2016). Modelling volatility on Karachi Stock Exchange, Pakistan. Journal of Asia Business Studies. 1-34.
Alberg, D., Shalit, H., & Yosef, R. (2008). Estimating stock market volatility using asymmetric GARCH models. Applied Financial Economics, 18(15), 1201-1208.
Ali Ahmed, H. J., Hassan, T., & Nasir, A. (2005). The relationship between trading volume, volatility and stock market returns: a test of mixed distribution hypothesis for a pre-and post crisis on Kuala Lumpur Stock Exchange. Investment Management and Financial Innovations, 2(3), 146-158.
Asemota, O. J., & Ekejiuba, U. C. (2017). An Application of Asymmetric GARCH Models on Volatility of Banks Equity in Nigeria’s Stock Market. CBN Journal of Applied Statistics. 8 (1), 73-99.
Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian journal of statistics, 171-178.
Banumathy, K., & Azhagaiah, R. (2015). Modelling Stock Market Volatility: Evidence from India. Managing Global Transitions: International Research Journal, 13(1), 28-42.
Black, F. (1976). Studies of stock price volatility of changes. American Statistical Association Journal. 177-181.
Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345-370.
Bucevska, V. (2013). An Empirical evaluation of GARCH models in value-at-risk estimation: Evidence from the Macedonian stock exchange. Business systems research journal: international journal of the Society for Advancing Business & Information Technology (BIT), 4(1), 49-64.
Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological methods & research, 33(2), 261-304.
Chan, S., Chu, J., Nadarajah, S., & Osterrieder, J. (2017). A statistical analysis of cryptocurrencies. Journal of Risk and Financial Management, 10(2), 12..
Cheteni, P. (2016). Stock market volatility using GARCH models: Evidence from South Africa and China stock markets. 4-12.
Ding, Z., Granger, C. W., & Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of empirical finance, 1(1), 83-106.
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 50 (4), 987-1007.
Engle, R. F., & Bollerslev, T. (1986). Modelling the persistence of conditional variances. Econometric reviews, 5(1), 1-50.
Engle, R. F., & Ng, V. K. (1993). Measuring and testing the impact of news on volatility. The journal of finance, 48(5), 1749-1778.
Engle, R. F., Lilien, D. M., & Robins, R. P. (1987). Estimating time varying risk premia in the term structure: The ARCH-M model. Econometrica: journal of the Econometric Society, 391-407.
Fang, J., Nakamura, H., & Maeda, H. (2011). The EPR effect: unique features of tumor blood vessels for drug delivery, factors involved, and limitations and augmentation of the effect. Advanced drug delivery reviews, 63(3), 136-151.
Fernández, C., & Steel, M. F. (1998). On Bayesian modeling of fat tails and skewness. Journal of the American Statistical Association, 93(441), 359-371.
Floros, C. (2008). Modelling volatility using GARCH models: evidence from Egypt and Israel. Middle Eastern Finance and Economics, (2), 31-41.
Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The journal of finance, 48(5), 1779-1801.
Gosset, W. S. (1908). Probable error of a correlation coefficient. Biometrika, 6(2-3), 302-310.
Goudarzi, H., & Ramanarayanan, C. S. (2010). Modeling and estimation of volatility in the Indian stock market. International Journal of Business and Management, 5(2), 85.
Hameed, A., Ashraf, H., & Siddiqui, R. (2006). Stock Market Volatility and Weak-form Efficiency: Evidence from an Emerging Market [with Comments]. The Pakistan Development Review, 1029-1040.
Hannan, E. J., & Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society. Series B (Methodological), 190-195.
Hassan, H. E., Mercer, S. L., Cunningham, C. W., Coop, A., & Eddington, N. D. (2009). Evaluation of the P-glycoprotein (Abcb1) affinity status of a series of morphine analogs: comparative study with meperidine analogs to identify opioids with minimal P-glycoprotein interactions. International journal of pharmaceutics, 375(1-2), 48-54.
Higgins, M. L., & Bera, A. K. (1992). A class of nonlinear ARCH models. International Economic Review, 137-158.
Hung , N. T. (2018). An empirical analysis of Euro Hungarian Forint exchange rate volatility using GARCH. Challenges in National and International Economic Policies. 57–67.
Jarque, C. M., & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review/Revue Internationale de Statistique, 163-172.
Jyothi , U., & Suresh, K. (2014). Estimating Stock Market Volatility Using Non-linear Models . IOSR Journal of Business and Management (IOSR-JBM). 62-65.
Kanasro, H. A., Rohra, C. L., & Junejo, M. A. (2009). Measurement of stock market volatility through ARCH and GARCH models: a case study of Karachi stock exchange. Australian Journal of Basic and Applied Sciences, 3(4), 3123-3127.
Karmakar, M. (2005). Modeling conditional volatility of the Indian stock markets. Vikalpa, 30(3), 21-38.
Khan, N. (2011). Dividend policy and the stock market reaction to dividend announcements in Pakistan (Doctoral dissertation, University of Dundee).
Kumar , H. P., & Patil , B. S. (August 2016 ). Volatility Forecasting- A Performance Measure of GARCH Techniques with Different Distribution Models. International Journal of Soft Computing, Mathematics and Control (IJSCMC), 5(No), 1-13.
Lim, C. M., & Sek, S. K. (2013). Comparing the performances of GARCH-type models in capturing the stock market volatility in Malaysia. Procedia Economics and Finance, 5, 478-487.
Ling, S., & McAleer, M. (2003). Asymptotic theory for a vector ARMA-GARCH model. Econometric theory, 19(2), 280-310.
Mwita, P. N., & Nassiuma, D. K. (2015). Volatility estimation of stock prices using Garch method. Kabarak Journal of Research & Innovation, 3(1), 48-53.
Najjar, M., Saleh, D., Zelic, M., Nogusa, S., Shah, S., Tai, A., ... & Whalen, M. J. (2016). RIPK1 and RIPK3 kinases promote cell-death-independent inflammation by Toll-like receptor 4. Immunity, 45(1), 46-59.
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica: Journal of the Econometric Society, 347-370.
Olbrys, J. (2013). Price and volatility spillovers in the case of stock markets located in different time zones. Emerging Markets Finance and Trade, 49(sup2), 145-157.
Omorogbe, J. A., Mc Nally, M., Cretu, I., & O'Connor, A. (2017). Mo1181 Gastric Intestinal Metaplasia Outcomes: Results From a 17 Year Tertiary Centre Upper GI Surveillance Programme in Ireland. Gastrointestinal Endoscopy, 85(5), AB452-AB453.
Peters, J. P. (2001). Estimating and forecasting volatility of stock indices using asymmetric GARCH models and (Skewed) Student-t densities. Preprint, University of Liege, Belgium, 3, 19-34.
Poon, S. H., & Granger, C. W. (2003). Forecasting volatility in financial markets: A review. Journal of economic literature, 41(2), 478-539.
Saeed, A. F., Wang, R., Ling, S., & Wang, S. (2017). Antibody engineering for pursuing a healthier future. Frontiers in microbiology, 8, 495.
Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, 6(2), 461-464.
Shah, A., Shahf, A. H., Parveen, N., Rehman, Z. U., Khan, S. Z., Rana, U. A., ... & Qureshi, R. (2016). Synthesis and electrochemical investigations of piperazines. Electrochimica Acta, 220, 705-711.
Stoyanov, J. V., Gantenbein-Ritter, B., Bertolo, A., Aebli, N., Baur, M., Alini, M., & Grad, S. (2011). Role of hypoxia and growth and differentiation factor-5 on differentiation of human mesenchymal stem cells towards intervertebral nucleus pulposus-like cells. Eur Cell Mater, 21(533), e47.
Taylor, S. J. (2008). Modelling financial time series. world scientific.
Theodossiou, P. (1998). Financial data and the skewed generalized t distribution. Management Science, 44(12-part-1), 1650-1661.
Vijayalakshmi, S., & Gaur, S. (2013). Modelling volatility: Indian stock and foreign exchange markets. Journal of Emerging Issues in Economics, Finance and Banking, 2(1), 583-98.
Wennström, A. (2014). Volatility Forecasting Performance: Evaluation of GARCH type volatility models on Nordic equity indices.
Wilhelmsson, A. (2006). Garch Forecasting Performance under Different Distribution Assumptions. Journal of Forecasting, 25, 561–578.
Zakoian, J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and control, 18(5), 931-955.
Published
2018-12-27
How to Cite
Naseem, S., fu, G. lei, Mohsin, M., Zia-ur-Rehman, M., & Baig, S. (2018). Volatility of pakistan stock market: A comparison of Garch type models with five distribution. Amazonia Investiga, 7(17), 486-504. Retrieved from https://www.amazoniainvestiga.info/index.php/amazonia/article/view/763
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