The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Estimation of VaR and Expected Shortfall for Stock Returns

주식수익률의 VaR와 ES 추정: GARCH 모형과 GPD를 이용한 방법을 중심으로

  • Kim, Ji-Hyun (Department of Statistics and Actuarial Science, Soongsil University) ;
  • Park, Hwa-Young (Department of Statistics and Actuarial Science, Soongsil University)
  • 김지현 (숭실대학교 정보통계보험수리학과) ;
  • 박화영 (숭실대학교 정보통계보험수리학과)
  • Received : 20100500
  • Accepted : 20100600
  • Published : 2010.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

Various estimators of two risk measures of a specific financial portfolio, Value-at-Risk and Expected Shortfall, are compared for each case of 1-day and 10-day horizons. We use the Korea Composite Stock Price Index data of 20-year period including the year 2008 of the global financial crisis. Indexes of five foreign stock markets are also used for the empirical comparison study. The estimator considering both the heavy tail of loss distribution and the conditional heteroscedasticity of time series is of main concern, while other standard and new estimators are considered too. We investigate which estimator is best for the Korean stock market and which one shows the best overall performance.

금융 포트폴리오의 두 위험측도인 VaR와 ES에 대한 여러 추정방법을 1일 후와 10일 후의 경우로 나누어 각각 비교하였다. 2008년 미국발 세계 금융위기 기간을 포함한 KOSPI 자료와 해외 5개국의 종합주가지수 자료를 이용하여 실증적으로 비교하였다. 손실 분포의 두터운 꼬리와 조건부 이분산성을 동시에 고려하는 방법을 중심으로 여러 방법을 추가적으로 고려하였고, 국내 자료에 어떤 방법이 적절하며 종합적인 성능은 어떤가를 살펴보았다.

Keywords

References

  1. 문성주, 양성국 (2006). 이분산성 및 두꺼운 꼬리분포를 가진 금융시계열의 위험추정: VaR와 ES를 중심으로, <재무관리연구>, 23, 189-208.
  2. Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999). Coherent measures of risk, Mathematical Finance, 9, 203-228. https://doi.org/10.1111/1467-9965.00068
  3. Balkema, A. A. and de Haan, L. (1974). Residual lifetime at great age, Annals of Probability, 2, 792-804. https://doi.org/10.1214/aop/1176996548
  4. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  5. Fama, E. F. (1965). The behavior of stock market prices, Journal of Business, 38, 34-105. https://doi.org/10.1086/294743
  6. Frey, R. and McNeil, A. (2002). VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights, Journal of Banking and Finance, 26, 1317-1334. https://doi.org/10.1016/S0378-4266(02)00265-0
  7. Gencay, R., Selcuk, F. and Ulugulyagci (2003). High volatility, thick tails and extreme value theory in VaR estimation, Insurance: Mathematics and Economics, 33, 337-356. https://doi.org/10.1016/j.insmatheco.2003.07.004
  8. McNeil, A. and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach, Journal of Empirical Finance, 7, 271-300. https://doi.org/10.1016/S0927-5398(00)00012-8
  9. McNeil, A., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton University Press.
  10. McNeil, A. and Saladin, T. (1997). The peaks over thresholds method for estimaing high quantiles of loss distributions, Proceedings of 28th International ASTIN Colloquium.
  11. McNeil, A. for S-Plus original; R port by Scott Ulman (2007). QRMlib: Provides R-language code to examine Quantitative Risk Management concepts. R package version 1.4.2. http://www.ma.hw.ac.uk/ mcneil/book/index.html.
  12. Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3, 119-131. https://doi.org/10.1214/aos/1176343003
  13. R Development Core Team (2008). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
  14. Rootzen, H. and Tajvidi, N. (1996). Extreme value statistics and wind storm losses: A case study, Scandinavian Actuarial Journal, 70-94.
  15. Seymour, A. and Polakow, D. (2003). A coupling of extreme-value theory and volatility updating with value-at-risk estimation in emerging markets: A South African test, Multinational Finance Journal, 7, 3-23. https://doi.org/10.17578/7-1/2-1

Cited by

  1. The GARCH-GPD in market risks modeling: An empirical exposition on KOSPI vol.27, pp.6, 2016, https://doi.org/10.7465/jkdi.2016.27.6.1661