응용통계연구 (The Korean Journal of Applied Statistics)

  • 제29권4호
  • /
  • Pages.689-697
  • /
  • 2016
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Vector at Risk와 대안적인 VaR

Vector at Risk and alternative Value at Risk

  • 홍종선 (성균관대학교, 통계학과) ;
  • 한수정 (성균관대학교, 통계학과) ;
  • 이기쁨 (성균관대학교, 통계학과)
  • Honga, C.S. (Department of Statistics, Sungkyunkwan University) ;
  • Han, S.J. (Department of Statistics, Sungkyunkwan University) ;
  • Lee, G.P. (Department of Statistics, Sungkyunkwan University)
  • 투고 : 2016.03.04
  • 심사 : 2016.04.26
  • 발행 : 2016.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

금융시장 위험관리 수단으로 많이 사용하는 기법 중의 하나는 Morgan이 제안한 최대손실금액을 추정하는 VaR (Value at Risk)이다. VaR은 한 산업의 금융위험 측정도구로 사용되어지지만 실제 생활에서는 여러 회사 또는 국내 전체의 산업의 VaR를 추정하는 경우가 많다. 따라서 투자할 여러 산업에 대하여 특정한 포트폴리오가 설정된 경우에 다변량분포에 대한 VaR를 추정하는 문제가 필요하다. 본 연구에서는 다변량분포에 대한 VaR를 추정하기 위하여, 다차원 분위 벡터를 제안하고, 이를 바탕으로 다차원 공간에서의 Vector at Risk를 정의한다. 다변량분포에 대하여 특정한 포트폴리오가 설정된 경우에, Vector at Risk 중에서의 한 점을 가장 적절한 VaR로 설정하는 방법을 제안한다. 이를 대안적인 VaR이라고 정의하고, 다변량 분포에 대한 이 방법에 대하여 토론한다. 2변량과 3변량의 예제를 통해 본 연구의 대안적인 VaR과 Morgan의 VaR를 각각 구하고, 비교 설명하면서 대안적인 VaR의 특징을 탐색한다.

The most useful method for financial market risk management may be Value at Risk (VaR) which estimates the maximum loss amount statistically. The VaR is used as a risk measure for one industry. Many real cases estimate VaRs for many industries or nationwide industries; consequently, it is necessary to estimate the VaR for multivariate distributions when a specific portfolio is established. In this paper, the multivariate quantile vector is proposed to estimate VaR for multivariate distribution, and the Vector at Risk for multivariate space is defined based on the quantile vector. When a weight vector for a specific portfolio is given, one point among Vector at Risk could be found as the best VaR which is called as an alternative VaR. The alternative VaR proposed in this work is compared with the VaR of Morgan with bivariate and trivariate examples; in addition, some properties of the alternative VaR are also explored.

키워드

참고문헌

  1. Andersson, F., Mausser, H., Rosen, D., and Uryasev, S. (2001). Credit risk optimization with condition value-at-risk, Mathematical Programming, 89, 273-291. https://doi.org/10.1007/PL00011399
  2. Barone-Adesi, G., Giannopoulos, K., and Vosper, L. (1999). VaR without correlations for portfolio of derivative securities, Journal of Futures Markets, 19, 583-602. https://doi.org/10.1002/(SICI)1096-9934(199908)19:5<583::AID-FUT5>3.0.CO;2-S
  3. Berkowitz, J., Christoffersen, P., and Pelletier, D. (2011). Evaluating Value-at-Risk models with desk-level data, Management Science, 57, 2213-2227. https://doi.org/10.1287/mnsc.1080.0964
  4. Chen, L. A. and Welsh, A. H. (2002). Distribution-function-based bivariate quantiles, Journal of Multivariate Analysis, 83, 208-231. https://doi.org/10.1006/jmva.2001.2043
  5. Heo, S. J., Yeo, S. C., and Kang, T. H. (2012). Performance analysis of economic VaR estimation using risk neutral probability distributions, Korean Journal of Applied Statistics, 25, 757-773. https://doi.org/10.5351/KJAS.2012.25.5.757
  6. Hong, C. S. and Kwon, T. W. (2010). Distribution fitting for the rate of return and value at risk, Journal of the Korean Data & Information Science Society, 21, 219-229.
  7. Hong, C. S. and Lee, J. H. (2011a). VaR estimation of multivariate distribution using Copula functions, Korean Journal of Applied Statistics, 24, 523-533. https://doi.org/10.5351/KJAS.2011.24.3.523
  8. Hong, C. S. and Lee, W. Y. (2011b). VaR estimation with multiple Copula functions, Korean Journal of Applied Statistics, 24, 809-820. https://doi.org/10.5351/KJAS.2011.24.5.809
  9. Jorion, P. (2007). Value at Risk, The New Benchmark for Market Risk (1st Ed.), McGraw-Hill, New York.
  10. Kang, M. J., Kim, J. Y., Song, J. W., and Song, S. J. (2013). Value at Risk with peaks over threshold: comparison study of parameter estimation, Korean Journal of Applied Statistics, 26, 483-494. https://doi.org/10.5351/KJAS.2013.26.3.483
  11. Krokhmal, P., Palmquist, J., and Uryasev, S. (2002). Portfolio optimization with conditional Value-at-Risk objective and constraints, Journal of Risk, 4, 11-27.
  12. Kupiec, P. (1995). Techniques for verifying the accuracy of risk management models, Journal of Derivatives, 2, 73-84. https://doi.org/10.3905/jod.1995.407918
  13. Li, D. X. (1999). Value at Risk based on the volatility skewness and kurtosis, Available from: http://www.riskmetrics.com/research/working/var4mm.pdf, RiskMetrics Group.
  14. Longin, F. M. (2000). From value at risk to stress testing: the extreme value approach, Journal of Banking & Finance, 24, 1097-1130. https://doi.org/10.1016/S0378-4266(99)00077-1
  15. Longin F. M. (2001). Beyond the VaR, Journal of Derivatives, 8, 36-48. https://doi.org/10.3905/jod.2001.319161
  16. Lopez, J. A. (1998). Methods for evaluating Value-at-Risk estimates, Economic Policy Review, 4, 119-124.
  17. Morgan, J. P. (1996). RiskMetrics, Technical Document (4th Ed.), JP Morgan, New York.
  18. Neftci, S. N. (2000). Value-at-Risk calculation extreme events and tail estimation, Journal of Derivatives, 7, 23-37. https://doi.org/10.3905/jod.2000.319126
  19. Park, J. S. and Jung, M. S. (2002). Market risk management strategies through VaR, KISDI Research Papers, Fall 2002, KISDI.
  20. Park, K. H., Ko, K. Y., and Beak, J. S. (2013). An one-factor VaR model for stock portfolio, Korean Journal of Applied Statistics, 26, 471-481 https://doi.org/10.5351/KJAS.2013.26.3.471
  21. Rockafellar, R. T. and Uryasev, S. (2000). Optimization of conditional value-at-risk, Journal of Risk, 2, 21-41. https://doi.org/10.21314/JOR.2000.038
  22. Rockafellar, R. T. and Uryasev, S. (2002). Conditional value-at-risk for general loss distributions, Journal of Banking & Finance, 26, 1443-1471. https://doi.org/10.1016/S0378-4266(02)00271-6
  23. Seo, S. H. and Kim, S. G. (2010). Estimation of VaR using extreme losses, and back-testing: case study, Korean Journal of Applied Statistics, 23, 219-234. https://doi.org/10.5351/KJAS.2010.23.2.219
  24. Yeo, S. C. and Li, Z. (2015). Performance analysis of volatility models for estimating portfolio value at risk, Korean Journal of Applied Statistics, 28, 541-599. https://doi.org/10.5351/KJAS.2015.28.3.541
  25. Yuzhi, C. (2010). Multivariate quantile function models, Statistica Sinica, 20, 481-496.
  26. Zangari, P. (1996). An improved methodology for measuring VaR, RiskMetrics Monitor, 2, 7-25.

피인용 문헌

  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. Multivariate confidence region using quantile vectors vol.24, pp.6, 2017, https://doi.org/10.29220/CSAM.2017.24.6.641