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The GARCH-GPD in market risks modeling: An empirical exposition on KOSPI

  • Received : 2016.10.31
  • Accepted : 2016.11.24
  • Published : 2016.11.30

Abstract

Risk analysis is a systematic study of uncertainties and risks we encounter in business, engineering, public policy, and many other areas. Value at Risk (VaR) is one of the most widely used risk measurements in risk management. In this paper, the Korean Composite Stock Price Index data has been utilized to model the VaR employing the classical ARMA (1,1)-GARCH (1,1) models with normal, t, generalized hyperbolic, and generalized pareto distributed errors. The aim of this paper is to compare the performance of each model in estimating the VaR. The performance of models were compared in terms of the number of VaR violations and Kupiec exceedance test. The GARCH-GPD likelihood ratio unconditional test statistic has been found to have the smallest value among the models.

Keywords

References

  1. Aczel, A. D. and Sounderpandian, J. (2009). Complete business statistics, 7th Ed., McGraw-Hill, Boston, MA.
  2. Blattberg, R. C. and Gonedes, N. J. (1974). A comparison of the stable and student distributions as statistical models for stock prices. The Journal of Business, 47, 244-280. https://doi.org/10.1086/295634
  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. Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 39, 841-862. https://doi.org/10.2307/2527341
  5. Christoersen P. and Pelletier D. (2004). Backtesting Value-at-Risk: A duration-based approach. Journal of Empirical Finance, 2, 84-108.
  6. Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987-1007. https://doi.org/10.2307/1912773
  7. Fajardo, J., Farias, A., Ornelas and J. R. H. (2005). Analysing the use of generalized hyperbolic distributions to value at risk calculations. Brazilian Journal of Applied Economics, 9, 25-38.
  8. Ghalanos, A. (2015). Univariate GARCH Models, R package version 1.3-6, available at http://www.unstarched.net.
  9. Kim, J. H. and Park, H. Y. (2010). Estimation of VaR and expected shortfall for stock returns. Korean Journal of Applied Statistics, 23, 651-668. https://doi.org/10.5351/KJAS.2010.23.4.651
  10. Kim, W. H. (2011). An empirical analysis of KOSPI volatility using GARCH-ARJI model. Korean Journal of Applied Statistics, 24, 71-81. https://doi.org/10.5351/KJAS.2011.24.1.071
  11. Kim, W. H. (2014). Dependence structure of Korean nancial markets Using copula-GARCH model. Communications for Statistical Applications and Methods, 21, 445-459. https://doi.org/10.5351/CSAM.2014.21.5.445
  12. Kim, W. H. and Bang, S. B. (2014). Regime-dependent characteristics of KOSPI return. Communications for Statistical Applications and Methods, 21, 501-512. https://doi.org/10.5351/CSAM.2014.21.6.501
  13. Ko, K. Y. and Son, Y. S. (2015). Optimal portfolio and VaR of KOSPI200 using one-factor model. Journal of the Korean Data & Information Science Society, 26, 323-334. https://doi.org/10.7465/jkdi.2015.26.2.323
  14. Kwon, D. and Lee, T. (2014). Hedging effectiveness of KOSPI200 index futures through VECM-CC-GARCH model. Journal of the Korean Data & Information Science Society, 25, 1449-1466. https://doi.org/10.7465/jkdi.2014.25.6.1449
  15. McNeil, A. J. (1999). Extreme value theory for risk managers, Department Matehmatik ETH Zentrum, Available at www.sfu.ca/rjones/econ811/readings/McNeil.
  16. Nam, D. and Gup, B. E. (2003). A quantile-fitting approach to value at risk for options, Journal of Risk Finance, 5, 40-50. https://doi.org/10.1108/eb022978
  17. Park, S. and Baek, C. (2014). On multivariate GARCH model selection based on risk management. Journal of the Korean Data & Information Science Society, 25, 1333-1343. https://doi.org/10.7465/jkdi.2014.25.6.1333
  18. Vallena, C. and Askvik, H. (2014). Performance of fat-tailed Value at Risk, a comparison using back-testing on OMXS30, Master Thesis, Jonkoping University, Sweden.
  19. Walck, C. (1996). Hand-book on statistical distributions for experimentalists, Particle Physics Group Fysikum University of Stockholm.
  20. Wuertz, D. (2013). fExtremes: Rmetrics: Extreme nancial market data, R package version 3010.81, availableat http://www.rmetrics.org.

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