포트폴리오 VaR 측정을 위한 EVT-GARCH-코퓰러 모형의 성과분석 = Performance analysis of EVT-GARCH-Copula models for estimating portfolio Value at Risk

다국어 초록 (Multilingual Abstract)

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.

국문 초록 (Abstract)

금융기관의 위험관리를 위한 중요한 도구로서 현재 VaR가 널리 사용되고 있다. 본 논문에서는 코퓰러 함수들을 이용하여 극단치이론과 GARCH 모형을 결합한 일변량분포로부터 구축한 다변량분포들을 바탕으로 코스피, 다우존스, 상하이 그리고 니케이 지수들로 구성된 포트폴리오의 VaR 추정과 그 성과에 관해 논의하였다. 사후검증 결과 전체적으로 볼 때 가우시안, t, 클레이톤, 프랭크 코퓰러를 사용한 t-분포의 오차항을 가진 변동성 모형들이 포트폴리오 VaR의 측정에 적합한 모형들로 나타났으며, 특히 프랭크 코퓰러의 경우에 가장 우수한 성과를 나타내었다.

참고문헌 (Reference)

1 여성칠, "포트폴리오 VaR 측정을 위한 변동성 모형의 성과분석" 한국통계학회 28 (28): 541-559, 2015

2 여성칠, "코퓰러와 극단치이론을 이용한 위험척도의 추정 및 성과분석" 한국통계학회 19 (19): 481-504, 2006

3 Danielsson, J., "Value-at-risk and extreme returns" 60 : 239-270, 2000

4 Jorion, P., "Value at Risk" McGraw Hill 2007

5 Zakoian, J. M., "Threshold heteroscedastic models" 18 : 931-955, 1994

6 Longin, F. M., "The asymptotic distribution of extreme stock market returns" 69 : 383-408, 1996

7 Kupiec, P., "Techniques for verifying the accuracy of risk measurement models" 2 : 73-84, 1995

8 Danielsson, J., "Tail index and quantile estimation with very high frequency data" 4 : 241-257, 1997

9 Black, F., "Studies of stock market volatility changes" 177-181, 1976

10 Lee, S. H., "Performance Analysis of VaR estimates using EVT-GARCH-Copula model" Konkuk University 2016

11 여성칠, "Performance Analysis of VaR and ES Based on Extreme Value Theory" 한국통계학회 13 (13): 389-407, 2006

12 Glosten, L. R., "On the relation between the expected value and the volatility of the nominal excess return on stocks" 48 : 1779-1801, 1993

13 Joe, H., "Multivariate Models and Dependence Concepts" Chapman and Hall 1997

14 Taylor, S. J., "Modelling Financial Time Series" John Wiley & Sons 1986

15 Engle, R. F., "Modeling the persistence of conditional variances" 5 : 1-50, 1986

16 Poon, S.-H., "Modeling extreme value dependence in international stock markets" 13 : 929-953, 2003

17 Ghorbel, A., "Measure of financial risk using conditional extreme value copulas with EVT margins" 11 : 51-85, 2009

18 Alexander, C., "Market Risk Analysis IV: Value at Risk Models" John Wiley & Sons 2008

19 Bollerslev, T., "Generalized autoregressive conditional heteroskedasticity" 31 : 307-327, 1986

20 Longin, F. M., "From Value at Risk to stress testing: the extreme value approach" 24 : 1097-1130, 2000

21 Sklar, A., "Fonctions de repartition a n dimensions et leurs marges" 8 : 229-231, 1959

22 Longin, F. M., "Extreme correlation of international equity markets" 56 : 649-676, 2001

23 Christoffersen, P. F., "Evaluating interval forecasts" 39 : 841-864, 1998

24 McNeil, A. J., "Estimation of tail-related risk for heteroscedastic financial time series : an extreme value approach" 7 : 271-300, 2000

25 Hsu, C. -P., "Effectiveness of copula-extreme value theory in estimating Value-at-Risk : empirical evidence from Asian emerging markets" 39 : 447-468, 2011

26 Embrechts, P., "Correlation: pitfalls and alternatives" 5 : 69-71, 1999

27 Cherubini, U., "Copula Methods in Finance" John Wiley & Sons 2004

28 Dowd, K., "Beyond value at Risk: The new Science of Risk Management" John Wiley & Sons 1998

29 Engle, R. F., "Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation" 50 : 987-1006, 1982

30 Huang, S. -C., "Applying GARCH-EVT-Copula models for portfolio Value-at-Risk on G7 currency markets" 74 : 136-151, 2011

31 Ding, Z., "A long memory property of stock market returns and model" 1 : 83-106, 1993