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On Double Value at Risk

Author

Listed:
  • Wanbing Zhang

    (School of Science, Nanjing University of Science and Technology, Nanjing 210094, China)

  • Sisi Zhang

    (Securities Co., Ltd., Beijing 102627, China
    These authors contributed equally to this work.)

  • Peibiao Zhao

    (School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
    These authors contributed equally to this work.)

Abstract

Value at Risk (VaR) is used to illustrate the maximum potential loss under a given confidence level, and is just a single indicator to evaluate risk ignoring any information about income. The present paper will generalize one-dimensional VaR to two-dimensional VaR with income-risk double indicators. We first construct a double-VaR with ( μ , σ 2 ) (or ( μ , V a R 2 ) ) indicators, and deduce the joint confidence region of ( μ , σ 2 ) (or ( μ , V a R 2 ) ) by virtue of the two-dimensional likelihood ratio method. Finally, an example to cover the empirical analysis of two double-VaR models is stated.

Suggested Citation

  • Wanbing Zhang & Sisi Zhang & Peibiao Zhao, 2019. "On Double Value at Risk," Risks, MDPI, vol. 7(1), pages 1-22, March.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:31-:d:212298
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    References listed on IDEAS

    as
    1. Taylor, Nick & Dijk, Dick van & Franses, Philip Hans & Lucas, Andre, 2000. "SETS, arbitrage activity, and stock price dynamics," Journal of Banking & Finance, Elsevier, vol. 24(8), pages 1289-1306, August.
    2. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value‐at‐Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    3. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, University Library of Munich, Germany.
    4. Jeremy Berkowitz, 1999. "A coherent framework for stress-testing," Finance and Economics Discussion Series 1999-29, Board of Governors of the Federal Reserve System (U.S.).
    5. Chen, Rongda & Li, Cong & Wang, Weijin & Wang, Ze, 2014. "Empirical analysis on future-cash arbitrage risk with portfolio VaR," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 210-216.
    6. repec:cdl:ucsdec:qt06m3d6nv is not listed on IDEAS
    7. Linsmeier, Thomas J. & Pearson, Neil D., 1996. "Risk measurement: an introduction to value at risk," ACE Reports 14796, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
    8. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. Jean-Philippe Bouchaud & Marc Potters, 1999. "Worst fluctuation method for fast value-at-risk estimates," Science & Finance (CFM) working paper archive 9909245, Science & Finance, Capital Fund Management.
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