Document Type : Article

**Authors**

^{1}
School of Mathematics and Economics, Hubei University of Education, Wuhan 430205, P. R. China

^{2}
School of Science, Wuhan University of Technology, Wuhan 430070, P. R. China

^{3}
School of Mathematics and Statistics, Huanggang Normal University, Huanggang 438000, P. R. China

**Abstract**

The implementation of the Shenzhen-Hong Kong Stock Connect (SHSC) mechanism has realized the largest two-way opening of China's capital market, but also increased the transmission of risks. In order to analyze the impact of SHSC on the volatility of single market in Shenzhen or Hong Kong, this paper establishes the volatility models of stock markets in Shenzhen and Hong Kong based on the GARCH-type models with different perturbation terms. The pre-applicable test is made and the result shows that the return rate series of Shenzhen and Hong Kong stock markets are stable and heteroscedastic, and they meet the conditions of establishing the GARCH-type models. Then, the GARCH model and EGARCH model are established to analyze the volatility of stock markets in Shenzhen and Hong Kong respectively. The results show that the opening of SHSC has increased the short-term volatility of the stock markets in Shenzhen and Hong Kong and improved the efficiency of information transmission between these two stock markets. Moreover, influenced by SHSC, the leverage effect of Shenzhen stock market is increasing, while that of Hong Kong stock market is decreasing.

**Keywords**

References:

1. Cao, F.Q. "Reform, innovation and risk prevention of China's capital market", Finance Forum, 23(9), pp. 5-10 (2018).

2. Gui, H., Market Expectations of Shenzhen-Hong Kong Stock Connect, China Finance, 17, pp. 74-75 (2016).

3. Wang, Q.Y. and Chong, T.T.L. "Co-integrated or not? after the Shanghai-Hong Kong and Shenzhen-Hong Kong stock connection schemes", Economics Letters, 163, pp. 167-171 (2018).

4. Rao, C.J., Xiao, X.P., Goh, M., et al. "Compound mechanism design of supplier selection based on multiattribute auction and risk management of supply chain", Computers & Industrial Engineering, 105, pp. 63-75 (2017).

5. Qu, S.J., Zhou, Y.Y., Zhang, Y.L., et al. "Optimal strategy for a green supply chain considering shipping policy and default risk", Computers and Industrial Engineering, 131, pp. 172-186 (2019).

6. Engle, R.F. "Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. infalation", Econometrica, 50(4), pp. 987-1008 (1982).

7. Engle, R.F. and Victor, K.N. "Measuring and testing the impact of news on volatility", Journal of Finance, 48(5), pp. 1022-1082 (1993).

8. Engle, R.F., Lilien, D.M., and Robins, R.P. "Estimating time varying risk premia in the term structure: the ARCH-M model", Econometrica, 55(2), pp. 391-407 (1987).

9. Abdalla, S.Z.S. "Modelling exchange rate volatility using GARCH models: empirical evidence from Arab countries", International Journal of Economics and Finance, 4(3), pp. 216-229 (2012).

10. Omolo, S.A. "Modelling exchange rate volatility of KES/USD using GARCH-type models", Journal of Finance, 10(3), pp. 47-59 (2014).

11. Dai, Z.F., Zhou, H.T., Wen, F.H., et al. "Efficient predictability of stock return volatility: The role of stock market implied volatility", The North American Journal of Economics and Finance, 52, p. 101174 (2020).

12. Zhang, T.H., Yuan, Y., and Wu, X. "Is microblogging data reflected in stock market volatility? Evidence from Sina Weibo", Finance Research Letters, 32, p. 101173 (2020).

13. Baklaci, H.F., Aydogan, B., and Yelkenci, T. "Impact of stock market trading on currency market volatility spillovers", Research in International Business and Finance, 52, p. 101182 (2020).

14. Kawakatsu, H. "Matrix exponential GARCH", Journal of Econometrics, 134(1), pp. 95-128 (2006).

15. Glosten, L.R., Jagannathan, R., and Runkle, D.E. "On the relation between the expected value and the volatility of the nominal excess return on stocks", Journal of Finance, 38(5), pp. 1779-1801 (1993).

16. Zakoian, J.M. "Threshold heteroskedastic models", Journal of Economic Dynamics and Control, 18(5), pp. 931-955 (1994).

17. Baillie, R.T., Bollerslev, T., and Mikkelsen, H.O. "Fractionally integrated generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 74(1), pp. 3-30 (1996).

18. Bollerslev, T. "A conditionally heteroskedastic time series model for speculative prices and rates of return", Review of Economics and Statistics, 69(3), pp. 542- 547 (1987).

19. Nelson, D.B. "3-conditional heteroskedasticity in asset returns: a new approach", Econometrica, 59(2), pp. 37-64 (1996).

20. Fornari, F. and Mele, A. "Modeling the changing asymmetry of conditional variances", Economics Letters, 50(2), pp. 197-203 (1996).

21. Laopodis, N.T. "Monetary policy implications of volatility linkages among long-term interest rates", Journal of Economics and Finance, 24(2), pp. 160- 179 (2000).

22. Hung, J.C. "Intelligent threshhold GARCH model applied to stock market of transmissions that volatility", Proceedings of the International Conference on Convergence Information Technology, pp. 1523-1528 (2007).

23. Yu, H.H., Fang, L.B., and Sun, W.C. "Forecasting performance of global economic policy uncertainty for volatility of Chinese stock market", Physica A: Statistical Mechanics and Its Applications, 505(3), pp. 931-940 (2018).

24. Zhou, X.H. and Huang, Y. "Research on the volatility relationship between the stock markets of Shanghai and Shenzhen", Economics and Management Research, 8, pp. 77-82 (2008).

25. Jiang, T.H. "Reversal of asymmetric effect of stock market volatility in China - An empirical study based on VS-GARCH model", Modern Finance and Economics, 2, pp. 65-68 (2008).

26. Guo, H. "Analysis of Chinese stock market volatility: an empirical study based on RS-GARCH model", Financial Theory & Practice, 2, pp. 78-80 (2014).

27. Wang, M. and Wang, C.L. "Research on conditional value at risk based on return volatility and heavy tail - Evidence from CSI 300 index", Mathematics in Practice and Theory, 47(17), pp. 70-76 (2017).

28. Zheng, Z.X., Wang, H.R., and Zhu, F.M. "Studies on volatility features and jump behavior of Shanghai 50ETF market based on Levy-GARCH model", Chinese Journal of Management Science, 27(2), pp. 41-52 (2019).

29. Kim, H.Y. andWon, C.H. "Forecasting the volatility of stock price index: A hybrid model integrating LSTM with multiple GARCH-type models", Expert Systems with Applications, 1031, pp. 25-37 (2018).

30. Wang, L., Ma, F., Liu, J., et al. "Forecasting stock price volatility: New evidence from the GARCH-MIDAS model", International Journal of Forecasting, 36(2), pp. 684-694 (2020). DOI: https://doi.org/10.1016/j.ijforecast. 2019.08 .005.

31. Rao, C.J., Goh, M., Zhao, Y., et al. "Location selection of sustainability city logistics centers", Transportation Research Part D: Transport and Environment, 36, pp. 29-44 (2015).

32. Xiao, Q.Z., Chen, L., Xie, M., et al. "Optimal contract design in sustainable supply chain: interactive impacts of fairness concern and overconfidence", Journal of the Operational Research Society, 72(7), pp. 1505-1524 (2021). DOI: 10.1080/01605682.2020.1727784.

33. Zhou, W. and Xu, Z.S. "Envelopment analysis, preference fusion, and membership improvement of intuitionistic fuzzy numbers", IEEE Transactions on Fuzzy Systems, 28(9), pp. 2119-2130 (2020). DOI:10.1109/TFUZZ.2019.2930483.

34. Rao, C.J., Lin, H., and Liu, M. "Design of comprehensive evaluation index system for P2P credit risk of "three rural" borrowers", Soft Computing, 24(15), pp. 11493-11509 (2020). DOI: 10.1007/s00500-019-04613-z.

35. Wang, M.T., Lu, L., and Song, K. "Impacts of policy factors on volatility of stock markets", Journal of Management Sciences in China, 15(12), pp. 40-57 (2012).

36. Liu, J., Ma, F., and Zhang, Y.J. "Forecasting the Chinese stock volatility across global stock markets", Physica A: Statistical Mechanics and Its Applications, 525, pp. 466-477 (2019).

37. Liu, L. and Pan, Z.Y. "Forecasting stock market volatility: The role of technical variables", Economic Modelling, 84, pp. 55-65 (2020).

38. Tian, C. and Peng, J.J. "An integrated picture fuzzy ANP-TODIM multi-criteria decision-making approach for tourism attraction recommendation", Technological and Economic Development of Economy, 26(2), pp. 331-354 (2020). DOI: https://doi.org/10.3846/tede.2019.11412.

39. Corbet, S., Gurdgiev, C., and Meegan, A. "Longterm stock market volatility and the influence of terrorist attacks in Europe", The Quarterly Review of Economics and Finance, 68, pp. 118-131 (2018).

40. Adel Rastkhiz, S.E., Mobini Dehkordi, A., Jahangiri Farsi, Y., et al. "A new approach to evaluating entrepreneurial opportunities", Journal of Small Business and Enterprise Development, 26(1), pp. 67-84 (2018).

41. Fang, L.B., Guo, B.S., and Zeng, Y. "The effect of skewness parameter on the performance of GARCH family when making estimation and prediction", Statistical Research, 31(10), pp. 106-112 (2014).

42. Li, F.S. "Does margin trading aggravate stock market fluctuation? From the perspective of asymmetric volatility", Journal of Financial Research, 440(2), pp. 147-162 (2017).

43. Lee, O. "V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model", Statistics & Probability Letters, 82(4), pp. 812-817 (2012).

44. Yang, H. and Wu, X.G. "Semiparametric EGARCH model with the case study of China stock market", Economic Modelling, 28(3), pp. 761-766 (2011).

45. Do, A., Powell, R. Yong, J., et al. "Time-varying asymmetric volatility spillover between global markets and China's A, B and H-shares using EGARCH and DCCEGARCH models", The North American Journal of Economics and Finance, 54, p. 101096 (2020). DOI: https://doi.org/10.1016/j.najef.2019.101096.

2. Gui, H., Market Expectations of Shenzhen-Hong Kong Stock Connect, China Finance, 17, pp. 74-75 (2016).

3. Wang, Q.Y. and Chong, T.T.L. "Co-integrated or not? after the Shanghai-Hong Kong and Shenzhen-Hong Kong stock connection schemes", Economics Letters, 163, pp. 167-171 (2018).

4. Rao, C.J., Xiao, X.P., Goh, M., et al. "Compound mechanism design of supplier selection based on multiattribute auction and risk management of supply chain", Computers & Industrial Engineering, 105, pp. 63-75 (2017).

5. Qu, S.J., Zhou, Y.Y., Zhang, Y.L., et al. "Optimal strategy for a green supply chain considering shipping policy and default risk", Computers and Industrial Engineering, 131, pp. 172-186 (2019).

6. Engle, R.F. "Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. infalation", Econometrica, 50(4), pp. 987-1008 (1982).

7. Engle, R.F. and Victor, K.N. "Measuring and testing the impact of news on volatility", Journal of Finance, 48(5), pp. 1022-1082 (1993).

8. Engle, R.F., Lilien, D.M., and Robins, R.P. "Estimating time varying risk premia in the term structure: the ARCH-M model", Econometrica, 55(2), pp. 391-407 (1987).

9. Abdalla, S.Z.S. "Modelling exchange rate volatility using GARCH models: empirical evidence from Arab countries", International Journal of Economics and Finance, 4(3), pp. 216-229 (2012).

10. Omolo, S.A. "Modelling exchange rate volatility of KES/USD using GARCH-type models", Journal of Finance, 10(3), pp. 47-59 (2014).

11. Dai, Z.F., Zhou, H.T., Wen, F.H., et al. "Efficient predictability of stock return volatility: The role of stock market implied volatility", The North American Journal of Economics and Finance, 52, p. 101174 (2020).

12. Zhang, T.H., Yuan, Y., and Wu, X. "Is microblogging data reflected in stock market volatility? Evidence from Sina Weibo", Finance Research Letters, 32, p. 101173 (2020).

13. Baklaci, H.F., Aydogan, B., and Yelkenci, T. "Impact of stock market trading on currency market volatility spillovers", Research in International Business and Finance, 52, p. 101182 (2020).

14. Kawakatsu, H. "Matrix exponential GARCH", Journal of Econometrics, 134(1), pp. 95-128 (2006).

15. Glosten, L.R., Jagannathan, R., and Runkle, D.E. "On the relation between the expected value and the volatility of the nominal excess return on stocks", Journal of Finance, 38(5), pp. 1779-1801 (1993).

16. Zakoian, J.M. "Threshold heteroskedastic models", Journal of Economic Dynamics and Control, 18(5), pp. 931-955 (1994).

17. Baillie, R.T., Bollerslev, T., and Mikkelsen, H.O. "Fractionally integrated generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 74(1), pp. 3-30 (1996).

18. Bollerslev, T. "A conditionally heteroskedastic time series model for speculative prices and rates of return", Review of Economics and Statistics, 69(3), pp. 542- 547 (1987).

19. Nelson, D.B. "3-conditional heteroskedasticity in asset returns: a new approach", Econometrica, 59(2), pp. 37-64 (1996).

20. Fornari, F. and Mele, A. "Modeling the changing asymmetry of conditional variances", Economics Letters, 50(2), pp. 197-203 (1996).

21. Laopodis, N.T. "Monetary policy implications of volatility linkages among long-term interest rates", Journal of Economics and Finance, 24(2), pp. 160- 179 (2000).

22. Hung, J.C. "Intelligent threshhold GARCH model applied to stock market of transmissions that volatility", Proceedings of the International Conference on Convergence Information Technology, pp. 1523-1528 (2007).

23. Yu, H.H., Fang, L.B., and Sun, W.C. "Forecasting performance of global economic policy uncertainty for volatility of Chinese stock market", Physica A: Statistical Mechanics and Its Applications, 505(3), pp. 931-940 (2018).

24. Zhou, X.H. and Huang, Y. "Research on the volatility relationship between the stock markets of Shanghai and Shenzhen", Economics and Management Research, 8, pp. 77-82 (2008).

25. Jiang, T.H. "Reversal of asymmetric effect of stock market volatility in China - An empirical study based on VS-GARCH model", Modern Finance and Economics, 2, pp. 65-68 (2008).

26. Guo, H. "Analysis of Chinese stock market volatility: an empirical study based on RS-GARCH model", Financial Theory & Practice, 2, pp. 78-80 (2014).

27. Wang, M. and Wang, C.L. "Research on conditional value at risk based on return volatility and heavy tail - Evidence from CSI 300 index", Mathematics in Practice and Theory, 47(17), pp. 70-76 (2017).

28. Zheng, Z.X., Wang, H.R., and Zhu, F.M. "Studies on volatility features and jump behavior of Shanghai 50ETF market based on Levy-GARCH model", Chinese Journal of Management Science, 27(2), pp. 41-52 (2019).

29. Kim, H.Y. andWon, C.H. "Forecasting the volatility of stock price index: A hybrid model integrating LSTM with multiple GARCH-type models", Expert Systems with Applications, 1031, pp. 25-37 (2018).

30. Wang, L., Ma, F., Liu, J., et al. "Forecasting stock price volatility: New evidence from the GARCH-MIDAS model", International Journal of Forecasting, 36(2), pp. 684-694 (2020). DOI: https://doi.org/10.1016/j.ijforecast. 2019.08 .005.

31. Rao, C.J., Goh, M., Zhao, Y., et al. "Location selection of sustainability city logistics centers", Transportation Research Part D: Transport and Environment, 36, pp. 29-44 (2015).

32. Xiao, Q.Z., Chen, L., Xie, M., et al. "Optimal contract design in sustainable supply chain: interactive impacts of fairness concern and overconfidence", Journal of the Operational Research Society, 72(7), pp. 1505-1524 (2021). DOI: 10.1080/01605682.2020.1727784.

33. Zhou, W. and Xu, Z.S. "Envelopment analysis, preference fusion, and membership improvement of intuitionistic fuzzy numbers", IEEE Transactions on Fuzzy Systems, 28(9), pp. 2119-2130 (2020). DOI:10.1109/TFUZZ.2019.2930483.

34. Rao, C.J., Lin, H., and Liu, M. "Design of comprehensive evaluation index system for P2P credit risk of "three rural" borrowers", Soft Computing, 24(15), pp. 11493-11509 (2020). DOI: 10.1007/s00500-019-04613-z.

35. Wang, M.T., Lu, L., and Song, K. "Impacts of policy factors on volatility of stock markets", Journal of Management Sciences in China, 15(12), pp. 40-57 (2012).

36. Liu, J., Ma, F., and Zhang, Y.J. "Forecasting the Chinese stock volatility across global stock markets", Physica A: Statistical Mechanics and Its Applications, 525, pp. 466-477 (2019).

37. Liu, L. and Pan, Z.Y. "Forecasting stock market volatility: The role of technical variables", Economic Modelling, 84, pp. 55-65 (2020).

38. Tian, C. and Peng, J.J. "An integrated picture fuzzy ANP-TODIM multi-criteria decision-making approach for tourism attraction recommendation", Technological and Economic Development of Economy, 26(2), pp. 331-354 (2020). DOI: https://doi.org/10.3846/tede.2019.11412.

39. Corbet, S., Gurdgiev, C., and Meegan, A. "Longterm stock market volatility and the influence of terrorist attacks in Europe", The Quarterly Review of Economics and Finance, 68, pp. 118-131 (2018).

40. Adel Rastkhiz, S.E., Mobini Dehkordi, A., Jahangiri Farsi, Y., et al. "A new approach to evaluating entrepreneurial opportunities", Journal of Small Business and Enterprise Development, 26(1), pp. 67-84 (2018).

41. Fang, L.B., Guo, B.S., and Zeng, Y. "The effect of skewness parameter on the performance of GARCH family when making estimation and prediction", Statistical Research, 31(10), pp. 106-112 (2014).

42. Li, F.S. "Does margin trading aggravate stock market fluctuation? From the perspective of asymmetric volatility", Journal of Financial Research, 440(2), pp. 147-162 (2017).

43. Lee, O. "V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model", Statistics & Probability Letters, 82(4), pp. 812-817 (2012).

44. Yang, H. and Wu, X.G. "Semiparametric EGARCH model with the case study of China stock market", Economic Modelling, 28(3), pp. 761-766 (2011).

45. Do, A., Powell, R. Yong, J., et al. "Time-varying asymmetric volatility spillover between global markets and China's A, B and H-shares using EGARCH and DCCEGARCH models", The North American Journal of Economics and Finance, 54, p. 101096 (2020). DOI: https://doi.org/10.1016/j.najef.2019.101096.

Transactions on Industrial Engineering (E)

January and February 2022Pages 372-386