Advertisement

Conditional ASGT-GARCH Approach to Value-at-Risk

  • Emrah AltunEmail author
  • Hüseyin Tatlıdil
  • Gamze Özel
Research Paper

Abstract

Most of the Value-at-Risk (VaR) models assume that asset returns are normally distributed, despite the fact that they are commonly known to be left skewed, fat-tailed and excess kurtosis. Forecasting VaR with misspecified model leads to the underestimation or overestimation of the true VaR. This paper proposes a new conditional model to forecast VaR by employing the alpha-skew generalized T (ASGT) distribution to GARCH models. ASGT distribution, introduced by Acitas et al. (Revista Colombiana de Estadistica 38(2):353–370, 2015), allows to model skewness, leptokurtosis and fat tail properties of conditional distribution of asset returns. ISE-100 index is used to examine the one-day-ahead VaR forecasting ability of the GARCH model under normal, Student’s t, generalized error, generalized T, skewed generalized T and ASGT innovation distributions. Empirical results show that the ASGT provides a superior fit to the conditional distribution of the log-returns followed by normal, Student’s t, generalized error, generalized T and skewed generalized T distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with ASGT error distribution, generates the most reliable VaR forecasts followed by other competitive models for a long position. As a result of this study, we conclude that the effects of skewness and fat-tails are more important in terms of forecasting true VaR than only the effect of fat-tails on VaR forecasts.

Keywords

GARCH models Alpha-Skew generalized T distribution Value-at-risk 

References

  1. Acitas S, Senoglu B, Arslan O (2015) Alpha-skew generalized t distribution. Revista Colombiana de Estadistica 38(2):353–370MathSciNetGoogle Scholar
  2. Anscombe FJ, Glynn WJ (1983) Distribution of the kurtosis statistic b 2 for normal samples. Biometrika 70(1):227–234MathSciNetzbMATHGoogle Scholar
  3. Angelidis T, Benos A, Degiannakis S (2004) The use of GARCH models in VaR estimation. Stat Methodol 1(1):105–128zbMATHGoogle Scholar
  4. Arellano-Valle RB, Cortes MA, Gomez HW (2010) An extension of the epsilon-skew-normal distribution. Commun Stat Theory Methods 39(5):912–922MathSciNetzbMATHGoogle Scholar
  5. Bali TG, Theodossiou P (2007) A conditional-SGT-VaR approach with alternative GARCH models. Ann Oper Res 151(1):241–267MathSciNetzbMATHGoogle Scholar
  6. Braione M, Scholtes NK (2016) Forecasting Value-at-Risk under different distributional assumptions. Econometrics 4(3):1–27Google Scholar
  7. Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econom 31(3):307–327MathSciNetzbMATHGoogle Scholar
  8. Bollerslev T (1987) A conditionally heteroskedastic time series model for speculative prices and rates of return. Rev Econ Stat 69:542–547Google Scholar
  9. Bollerslev T, Engle RF, Nelson DB (1994) ARCH models. In Engle RF, McFadden DL (eds) Handbook of econometrics, vol. 4. Elsevier Science, North-Holland: Amsterdam, pp 2959–3038Google Scholar
  10. Christoffersen PF (1998) Evaluating interval forecasts. Int Econ Rev 39:841–862MathSciNetGoogle Scholar
  11. D’Agostino RB (1970) Transformation to normality of the null distribution of g1. Biometrika 57(3):679–681zbMATHGoogle Scholar
  12. Elal-Olivero D (2010) Alpha-skew-normal distribution. Proyecciones (Antofagasta) 29(3):224–240MathSciNetzbMATHGoogle Scholar
  13. Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econom J Econ Soc 50:987–1007MathSciNetzbMATHGoogle Scholar
  14. Harmantzis FC, Miao L, Chien Y (2006) Empirical study of value-at-risk and expected shortfall models with heavy tails. J Risk Finance 7(2):117–135Google Scholar
  15. Hung JC, Lee MC, Liu HC (2008) Estimation of value-at-risk for energy commodities via fat-tailed GARCH models. Energy Econ 30(3):1173–1191Google Scholar
  16. Kupiec PH (1995) Techniques for verifying the accuracy of risk measurement models. J Deriv 3(2):73–84Google Scholar
  17. Lee CF, Su JB (2012) Alternative statistical distributions for estimating value-at-risk: theory and evidence. Rev Quant Finance Account 39(3):309–331Google Scholar
  18. Lee MC, Su JB, Liu HC (2008) Value-at-risk in US stock indices with skewed generalized error distribution. Appl Financ Econ Lett 4(6):425–431Google Scholar
  19. Lopez JA (1999) Methods for evaluating value-at-risk estimates. Econ Rev Fed Reserve Bank San Franc 2:3Google Scholar
  20. Ma Y, Genton MG (2004) Flexible class of skew-symmetric distributions. Scand J Stat 31(3):459–468MathSciNetzbMATHGoogle Scholar
  21. McDonald JB, Newey WK (1988) Partially adaptive estimation of regression models via the generalized t distribution. Econ Theory 4(03):428–457MathSciNetGoogle Scholar
  22. Nelson D (1991) Conditional heteroscedasticity in asset returns: a new approach. Econometrica 59:347–370MathSciNetzbMATHGoogle Scholar
  23. Piessens R, de Doncker-Kapenga E, Uberhuber CW, Kahaner DK (2012) Quadpack: a subroutine package for automatic integration, 1st edn. Springer Science & Business Media, BerlinzbMATHGoogle Scholar
  24. Rasekhi M, Chinipardaz R, Alavi SMR (2016) A flexible generalization of the skew normal distribution based on a weighted normal distribution. Stat Methods Appl 25(3):375–394MathSciNetzbMATHGoogle Scholar
  25. Theodossiou P (1998) Financial data and the skewed generalized t distribution. Mang Sci 44(12–part–1):1650–1661zbMATHGoogle Scholar
  26. Venkataraman S (1997) Value at risk for a mixture of normal distributions: the use of quasi-Bayesian estimation techniques. Econ Perspect Fed Reserve Bank Chicago 21:2–13Google Scholar
  27. Zangari P (1996) An improved methodology for measuring VaR. RiskMetrics Monit 2(1):7–25Google Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of StatisticsHacettepe UniversityAnkaraTurkey

Personalised recommendations