An Empirical Evaluation in GARCH Volatility Modeling: Evidence from the Stockholm Stock Exchange

Full-Text HTML XML Download Download as PDF (Size:1700KB) PP. 366-390
DOI: 10.4236/jmf.2017.72020    422 Downloads   555 Views  
Author(s)    Leave a comment

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.

Cite this paper

Dritsaki, C. (2017) An Empirical Evaluation in GARCH Volatility Modeling: Evidence from the Stockholm Stock Exchange. Journal of Mathematical Finance, 7, 366-390. doi: 10.4236/jmf.2017.72020.

References

[1] Marquardt, D.W. (1963) An Algorithm for Least Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics, 11, 431-441.
https://doi.org/10.1137/0111030
[2] Engle, R.F. (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of UK Inflation. Econometrica, 50, 987-1008.
https://doi.org/10.2307/1912773
[3] Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327.
https://doi.org/10.1016/0304-4076(86)90063-1
[4] Black, F. (1976) Studies in Stock Price Volatility Changes of the Nominal Excess Return on Stocks. Proceedings of the American Statistical Association, Business and Economics Statistics Section, 177-181.
[5] Nelson, D.B. (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59, 347-370.
https://doi.org/10.2307/2938260
[6] Glosten, L.R., Jagannathan, R. and 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, 1779-1801.
https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
[7] Donaldson, R.G. and Kamstra, M. (1997) An Artificial Neural Network—GARCH Model for International Stock Return Volatility. Journal of Empirical Finance, 4, 17-46.
https://doi.org/10.1016/s0927-5398(96)00011-4
[8] Nam, K., Pyun, C.S. and Arize, C.A. (2002) Asymmetric Mean-Reversion and Contrarian Profits: ANSTGARCH Approach. Journal of Empirical Finance, 9, 563-588.
https://doi.org/10.1016/S0927-5398(02)00011-7
[9] Tudor, C. (2008) Modeling Time Series Volatilities Using Symmetrical GARCH Models. The Romanian Economic Journal, 30, 183-208.
[10] Panait, I. and Slavescu, E.O. (2012) Using Garch-in-Mean Model to Investigate Volatility and Persistence at Different Frequencies for Bucharest Stock Exchange during 1997-2012. Theoretical and Applied Economics, 19, 55-76.
[11] Gao, Y., Zhang, C. and Zhang, L. (2012) Comparison of GARCH Models Based on Different Distributions. Journal of Computers, 7, 1967-1973.
https://doi.org/10.4304/jcp.7.8.1967-1973
[12] Dutta, A. (2014) Modelling Volatility: Symmetric or Asymmetric GARCH Models? Journal of Statistics: Advances in Theory and Applications, 12, 99-108.
[13] Bollerslev, T., Chou, R.Y. and Kroner, K.F. (1992) ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence. Journal of Econometrics, 52, 5-59.
https://doi.org/10.1016/0304-4076(92)90064-X
[14] Poon, S.H. and Granger C.W.J. (2003) Forecasting Volatility in Financial Markets: A Review. Journal of Economic Literature, 41, 478-539.
https://doi.org/10.1257/.41.2.478
[15] Engle, R.F. and Ng, V.K. (1993) Measuring and Testing the Impact of News on Volatility. Journal of Finance, 48, 1749-1778.
https://doi.org/10.1111/j.1540-6261.1993.tb05127.x
[16] Greene, W.H. (2012) Econometric Analysis. 7th Edition, Prentice Hall, Upper Saddle River.
[17] Brooks, C., Clare, A.D. and Persand G. (2000) A Word of Caution on Calculating Market Based Minimum Capital Risk Requirements. Journal of Banking and Finance, 24, 1557-1574.
https://doi.org/10.1016/S0378-4266(99)00092-8
[18] Vilasuso, J. (2002) Forecasting Exchange Rate Volatility, Economics Letters, 76, 59-64.
https://doi.org/10.1016/S0165-1765(02)00036-8
[19] Bollerslev, T. (1987) Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. Review of Economics and Statistics, 69, 542-547.
https://doi.org/10.2307/1925546
[20] Ljung, G. and Box, G. (1978) On a Measure of Lack of Fit in Time Series Models. Biometrika, 65, 297-303.
https://doi.org/10.1093/biomet/65.2.297
[21] Ljung, G. and Box, G. (1979) The Likelihood Function of Stationary Autoregressive-Moving Average Models. Biometrika, 66, 265-270.
https://doi.org/10.1093/biomet/66.2.265
[22] Press, W., Flannery, B., Teukolsky, S. and Vettering, W. (1988) Numerical Recipes in C. Cambridge University Press, New York.
[23] Brooks, C. (2008) Introductory Econometrics for Finance. 2nd Edition, Cambridge University Press, New York.
https://doi.org/10.1017/CBO9780511841644
[24] Theil, H. (1961) Economic Forecasts and Policy. North-Holland Publishing Company, Amsterdam.
[25] Patton, A. (2006) Volatility Forecast Comparison Using Imperfect Volatility Proxies. University of Technology, Sydney.
[26] Vilhelmsson, A. (2006) Garch Forecasting Performance under Different Distribution Assumptions. Journal of Forecasting, 25, 561-578.
https://doi.org/10.1002/for.1009
[27] Hamilton, J.D. and Susmelb, R. (1994) Autoregressive Conditional Heteroskedasticity and Changes in Regime. Journal of Econometrics, 64, 307-333.
https://doi.org/10.1016/0304-4076(94)90067-1
[28] Poon, S.H. and Granger, C. (2003) Forecasting Volatility in Financial Markets: A Review. Journal of Economic Literature, 41, 478-539.
https://doi.org/10.1257/.41.2.478
[29] Kim, T.H. and White, H. (2004) On More Robust Estimation of Skewness and Kurtosis. Finance Research Letters, 1, 56-73.
https://doi.org/10.1016/S1544-6123(03)00003-5

  
comments powered by Disqus

Copyright © 2017 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.