DOI QR코드

DOI QR Code

Performance Analysis of Volatility Models for Estimating Portfolio Value at Risk

포트폴리오 VaR 측정을 위한 변동성 모형의 성과분석

  • Yeo, Sung Chil (Department of Applied Statistics, Konkuk University) ;
  • Li, Zhaojing (Department of Applied Statistics, Konkuk University)
  • 여성칠 (건국대학교 응용통계학과) ;
  • 이조청 (건국대학교 응용통계학과)
  • Received : 2015.03.30
  • Accepted : 2015.04.15
  • Published : 2015.06.30

Abstract

VaR is now widely used as an important tool to evaluate and manage financial risks. In particular, it is important to select an appropriate volatility model for the rate of return of financial assets. In this study, both univariate and multivariate models are considered to evaluate VaR of the portfolio composed of KOSPI, Hang-Seng, Nikkei indexes, and their performances are compared through back testing techniques. Overall, multivariate models are shown to be more appropriate than univariate models to estimate the portfolio VaR, in particular DCC and ADCC models are shown to be more superior than others.

Acknowledgement

Supported by : 건국대학교

References

  1. Brooks, C. and Persand, G. (2003). The effect of asymmetries on stock index return Value-at-Risk estimates, Journal of Risk Finance, 4, 29-42. https://doi.org/10.1108/eb022959
  2. Cappiello, L., Engle, R. F. and Sheppard, K. (2006). Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics, 4, 537-572. https://doi.org/10.1093/jjfinec/nbl005
  3. Cho, D. (2004). The effects of estimation methods of stock price volatility on VaR, Korean Journal of Futures and Options, 12, 1-24.
  4. Christoffersen, P. F. (1998). Evaluating interval forecasts, International Economic Review, 39, 841-864. https://doi.org/10.2307/2527341
  5. Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). A long memory property of stock market returns and model, Journal of Empirical Finance, 1, 83-106. https://doi.org/10.1016/0927-5398(93)90006-D
  6. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1006. https://doi.org/10.2307/1912773
  7. Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate GARCH models, Journal of Business and Economic Statistics, 20, 339-350. https://doi.org/10.1198/073500102288618487
  8. Engle, R. F. and Bollerslev, T. (1986). Modeling the persistence of conditional variances, Econometric Reviews, 5, 1-50. https://doi.org/10.1080/07474938608800095
  9. Engle, R. F. and Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH, Econometric Theory, 11, 122-150. https://doi.org/10.1017/S0266466600009063
  10. Fama, E. F. (1965). The behavior of stock market prices, Journal of Business, 38, 34-105. https://doi.org/10.1086/294743
  11. Glosten, L. R., Jaganathan, R. and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks, Journal of Finance, 48, 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
  12. Hwang, S. Y., Choi, M. S. and Do, J. D. (2009). Assessments for MGARCH models using back-testing: Case study, The Korean Journal of Applied Statistics, 22, 261-270. https://doi.org/10.5351/KJAS.2009.22.2.261
  13. Jorion, P. (2007). Value at Risk, 3rd edition, McGraw Hill, New York.
  14. Kupiec, P. (1995). Techniques for verifying the accuarcy of risk measurement models, Journal of Dervatives,, 2, 73-84. https://doi.org/10.3905/jod.1995.407918
  15. Lee, H. (2011). Volatility model fitness and VaR forecasting performance: A Korean study, The Korean Journal of Financial Management, 28, 115-148.
  16. Alexander, C. O. and Chibumba, A. M. (1997). Multivariate orthogonal factor GARCH, Mimeo, University of Sussex.
  17. Bauwens, L., Laurent, S. and rombouts, J. V. K. (2006). Multivariate garch models: A survey, Journal of Applied Econometrics, 21, 79-109. https://doi.org/10.1002/jae.842
  18. Berkowitz, J. and O'Brien, J. (2002). How accurate are Value-at-Risk models at commercial banks?, Journal of Finance, 57, 1093-1112. https://doi.org/10.1111/1540-6261.00455
  19. Black, F. (1976). Studies of stock market volatility changes, Proceedings of the American Statistical Association, Business and Economic Statistics Section, 177-181.
  20. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  21. Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates, A multivariate generalized ARCH model, Review of Economics and Statistics, 72, 498-505. https://doi.org/10.2307/2109358
  22. Bollerslev, T., Engle, R. F. and Wooldridge, J. M. (1988). A capital asset pricing model with time-varying covariances, The Journal of Political Economy, 96, 116-131. https://doi.org/10.1086/261527
  23. Lee, S. J. and Binh, K. B. (2008). Model selection for estimating portfolio VaR in Korean stock market, Asia-Pacific Journal of Financial Studies, 37, 877-913.
  24. Lopez, J. A. (1998). Testing your tests, The Financial Survey, May-June, 18-20.
  25. Lopez, J. A. (1999). Method for evaluating Value-at-Risk estimates, Federal Reserve Bank of San Francisco Economic Review, 2, 3-17.
  26. Mandelbrot, B. (1963). The variation of certain speculative prices, Journal of Business, 36, 394-419. https://doi.org/10.1086/294632
  27. McAleer, M. and da Veiga, B. (2008). Single-index and portfolio models for forecasting Value-at-Risk thresholds, Journal of Forecasting, 27, 217-235. https://doi.org/10.1002/for.1054
  28. Nelson, D. B. (1991). Conditional heteroscedasticity in asset returns: A new approach, Econometrica, 59, 347-370. https://doi.org/10.2307/2938260
  29. Park, R. H., Choi, M. S. and Hwang, S. Y. (2011). Asymmetric CCC modelling in multivariate-GARCH with illustrations of multivariate financial data, The Korean Journal of Applied Statistics, 24, 821-831. https://doi.org/10.5351/KJAS.2011.24.5.821
  30. Restrepo, M. I. (2012). Estimating portfolio Value-at-Risk with GARCH and MGARCH models, Perfil de Coyuntura Economica, 19, 77-92, Universidad de Antioquia.
  31. Rombouts, J. V. K. and Verbeek, M. (2009). Evaluating portfolio Value-at-Risk using semi-parametric GARCH models,Quantitative Finance,9, 737-745. Discussion Paper, Erasmus Research Institute of Management, Erasmus University Rotterdam. https://doi.org/10.1080/14697680902785284
  32. Silvennoinen, A. and Terasvirta, T. (2009). Multivariate GARCH models, Handbook of Financial Time Series, Andersen, T. G., Davis, R. A., Kreiss, J.-P. and Mikosch, T. V., Eds., Springer, 201-229.
  33. Sarma, M., Thomas, S. and Shah, A. (2003). Selection of Value-at-Risk models, Journal of Forecasting, 22, 337-358. https://doi.org/10.1002/for.868
  34. Tse, Y. K. and Tsui, A. K. C. (2002). A multivariate GARCH model with time-varying correlations, Journal of Business and Economic Statistics, 20, 351-362. https://doi.org/10.1198/073500102288618496
  35. Tsay, R. S. (2010). Analysis of Financial Time Series, 3rd ed., John Wiley and Sons, New Jersey.
  36. Zakoian, J. M. (1994). Threshold heteroscedastic models, Journal of Economic Dynamics and Control, 18, 931-955. https://doi.org/10.1016/0165-1889(94)90039-6
  37. Zivot, E. and Wang, J. (2006). Modelling Financial Time Series with S-plus, 2nd ed., Springer.

Cited by

  1. Properties of alternative VaR for multivariate normal distributions vol.27, pp.6, 2016, https://doi.org/10.7465/jkdi.2016.27.6.1453
  2. Performance analysis of EVT-GARCH-Copula models for estimating portfolio Value at Risk vol.29, pp.4, 2016, https://doi.org/10.5351/KJAS.2016.29.4.753
  3. Vector at Risk and alternative Value at Risk vol.29, pp.4, 2016, https://doi.org/10.5351/KJAS.2016.29.4.689