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

Atsmegiorgis, Cheru; Kim, Jongtae; Yoon, Sanghoo

doi:10.7465/jkdi.2016.27.6.1661

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

Journal of the Korean Data & Information Science Society = 한국데이터정보과학회지, v.27 no.6, 2016년, pp.1661 - 1671

Atsmegiorgis, Cheru (Department of Statistics, Daegu University) , Kim, Jongtae (Department of Computer Science and Statistics) , Yoon, Sanghoo (Department of Computer Science and Statistics)

Abstract ▼ AI-Helper

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.

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문제 정의

The aim of this paper is to compare performance of GARCH and GARCH-GPD models on the KOSPI data. In both models, the maximum likelihood estimation has been employed to estimate model parameters.
Moreover, there are researches like (Vallena and Askvik, 2014) on GARCH models that consider the generalized hyperbolic distribution for the residual. This paper considers the GARCH model with normal, t and generalized hyperbolic innovations for the residuals.

제안 방법

It is a tool that risk managers apply to check how well their forecasts on VaR are attuned. In this paper, dynamic back-testing is used to evaluate the performance of the models. The ugarchfit function and ugarchroll function in ‘rugarch’ package (Ghalanos, 2015), gpdFit function in ‘fExtreme’ package (Wuertz, 2013) of R program were used for analysis.
The aim of this paper is to examine and compare the ability of GARCH (Generalized Auto Regressive Conditional Heteroscedasticity) model with normal, t, generalized hyperbolic innovations and GARCH-EVT (Extreme Value Theory) modeling that are used for modeling the VaR. Moreover a detailed theoretical overview of both traditional VaR models and extreme value theory would be discussed.
The test is set up as a likelihood ratio test. Kupiecs unconditional coverage test statistic and Christoffersen converage test statistic are defined as

이론/모형

These residuals are conventionally assumed to be independently and identically distributed and to follow a normal distribution. The GARCH model with normal innovations is fitted using the pseudo maximum likelihood procedure. The original ARCH/GARCH models were based on the normal distribution of the residual terms.
For the generalized hyperbolic distribution, the shape of the distribution is determined by two parameters; the shape parameter which measures the peakedness, and the GHlambda parameter which relates to the tail fatness of the probability density function (Fajardo et al, 2005). The parameters of the models are estimated using the maximum likelihood method.

성능/효과

9% actual percentage for t distributed error. The VaR model with generalized hyperbolic error term accumulate 8 exceedances that is a 0.5% actual percentage, while the VaR model with GARCH models augmented with GPD model generated 14 exceedances which is 0.9% actual percentage.

참고문헌 (20)

Aczel, A. D. and Sounderpandian, J. (2009). Complete business statistics, 7th Ed., McGraw-Hill, Boston, MA.
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.

상세보기
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.

상세보기
Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 39, 841-862.

상세보기
Christoersen P. and Pelletier D. (2004). Backtesting Value-at-Risk: A duration-based approach. Journal of Empirical Finance, 2, 84-108.
Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987-1007.

상세보기
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.
Ghalanos, A. (2015). Univariate GARCH Models, R package version 1.3-6, available at http://www.unstarched.net.
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.

원문보기 상세보기
Kim, W. H. (2011). An empirical analysis of KOSPI volatility using GARCH-ARJI model. Korean Journal of Applied Statistics, 24, 71-81.

원문보기 상세보기
Kim, W. H. (2014). Dependence structure of Korean nancial markets Using copula-GARCH model. Communications for Statistical Applications and Methods, 21, 445-459.

원문보기 상세보기
Kim, W. H. and Bang, S. B. (2014). Regime-dependent characteristics of KOSPI return. Communications for Statistical Applications and Methods, 21, 501-512.

원문보기 상세보기
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.

원문보기 상세보기
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.

원문보기 상세보기
McNeil, A. J. (1999). Extreme value theory for risk managers, Department Matehmatik ETH Zentrum, Available at www.sfu.ca/rjones/econ811/readings/McNeil.
Nam, D. and Gup, B. E. (2003). A quantile-fitting approach to value at risk for options, Journal of Risk Finance, 5, 40-50.

상세보기
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.

원문보기 상세보기
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.
Walck, C. (1996). Hand-book on statistical distributions for experimentalists, Particle Physics Group Fysikum University of Stockholm.
Wuertz, D. (2013). fExtremes: Rmetrics: Extreme nancial market data, R package version 3010.81, availableat http://www.rmetrics.org.

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

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