Vector at Risk and alternative Value at Risk

Vector at Risk와 대안적인 VaR

  • Honga, C.S. (Department of Statistics, Sungkyunkwan University) ;
  • Han, S.J. (Department of Statistics, Sungkyunkwan University) ;
  • Lee, G.P. (Department of Statistics, Sungkyunkwan University)
  • 홍종선 (성균관대학교, 통계학과) ;
  • 한수정 (성균관대학교, 통계학과) ;
  • 이기쁨 (성균관대학교, 통계학과)
  • Received : 2016.03.04
  • Accepted : 2016.04.26
  • Published : 2016.06.30


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.


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