Skip to main content
SpringerLink
Log in

A New Risk Measure MMVaR: Properties and Empirical Research

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The paper presents the properties of an alternative method, which measures market risk over time-horizon exceeding one day: Mark to market value at risk (MMVaR). Relying on the minimal returns during the time interval, this method not only considers the non-normality of data and information about sample size, but also meets the requirement of increasing the minimal capital ratio in Basel III, basically. The authors theoretically prove the translation invariance, monotonicity and subadditivity of MMVaR as a risk measure under some conditions, and study its finite sample properties through Monte Carlo simulations. The empirical analysis shows that MMVaR can measure multi-period risk accurately.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. McAleer M, Jimenez-Martin J A, and Perez-Amaral T, GFC-robust risk management strategies under the Basel Accord, International Review of Economics & Finance, 2013, 27: 97–111.

    Article  MATH  Google Scholar 

  2. BCBS, International convergence of capital measurement and capital standards, Bank for International Settlements (BIS), 2006.

  3. Linsmeier T J and Pearson N D, Value at risk, Financial Analysts Journal, 2000, 56(2): 47–67.

    Article  Google Scholar 

  4. Gourieroux C and Jasiak J, Handbook of Financial Econometrics: Tools and Techniques, Elsevier, North-Holland, 2010.

    MATH  Google Scholar 

  5. Dowd K, Beyond Value at Risk: The New Science of Risk Management, John Wiley & Sons, Chichester, 1998.

    MATH  Google Scholar 

  6. Mandelbrot B, The stable paretian income distribution when the apparent exponent is near two, International Economic Review, 1963, 4(1): 111–115.

    Article  Google Scholar 

  7. Fama E F, The behavior of stock-market prices, The Journal of Business, 1965, 38(1): 34–105.

    Article  Google Scholar 

  8. Pagan A, The econometrics of financial markets, Journal of Empirical Finance, 1996, 3(1): 15–102.

    Article  MathSciNet  Google Scholar 

  9. LeBaron B and Samanta R, Extreme value theory and fat tails in equity markets, Computing in Economics and Finance, 2005, DOI: https://doi.org/10.2139/ssrn.873656.

  10. Miletic M and Miletic S, Performance of value at risk models in the midst of the global financial crisis in selected CEE emerging capital markets, Economic Research-Ekonomska Istraivanja, 2015, 28(1): 132–166.

    Article  Google Scholar 

  11. Menken O, Value at risk and self-similarity, Numerical Methods for Finance, Chapman and Hall/CRC, New York, 2007.

    Google Scholar 

  12. Provizionatou V, Markose S, and Menkens O, Empirical scaling rules for value-at-risk (VaR), Working paper, Centre for Computational Finance and Economic Agents (CCFEA), 2005.

  13. Danielsson J and Zigrand J P, On time-scaling of risk and the square-root-of-time rule, Journal of Banking & Finance, 2006, 30(10): 2701–2713.

    Article  Google Scholar 

  14. Wang J N, Yeh J H, and Cheng N Y P, How accurate is the square-root-of-time rule in scaling ail risk: A global study, Journal of Banking & Finance, 2011, 35(5): 1158–1169.

    Article  Google Scholar 

  15. Chen Y, Wang Z C, and Zhang Z J, Mark to market value at risk, Journal of Econometrics, 2019, 208(1): 299–321.

    Article  MathSciNet  MATH  Google Scholar 

  16. Cheridito P, Delbaen F, and Kupper M, Coherent and convex monetary risk measures for unbounded cadlag processes, Finance and Stochastics, 2005, 9(3): 369–387.

    Article  MathSciNet  MATH  Google Scholar 

  17. Frittelli M and Scandolo G, Risk measures and capital requirements for processes, Mathematical Finance, 2006, 16(4): 589–612.

    Article  MathSciNet  MATH  Google Scholar 

  18. Meng Z Q, Jiang M, and Hu Q Y, Dynamic cvar with multi-period risk problems, Journal of Systems Science and Complexity, 2011, 24(5): 907–918.

    Article  MathSciNet  MATH  Google Scholar 

  19. Cheridito P and Kupper M, Composition of time-consistent dynamic monetary risk measures in discrete time, International Journal of Theoretical and Applied Finance, 2011, 14(1): 137–162.

    Article  MathSciNet  MATH  Google Scholar 

  20. Danielsson J, Jorgensen B N, Samorodnitsky G, et al., Fat tails, var and subadditivity, Journal of Econometrics, 2013, 172(2): 283–291.

    Article  MathSciNet  MATH  Google Scholar 

  21. Artzner P, Delbaen F, Eber J M, et al., Coherent measures of risk, Mathematical Finance, 1999, 9(3): 203–228.

    Article  MathSciNet  MATH  Google Scholar 

  22. Feller W, An Introduction to Probability Theory and Its Applications, John Wiley & Sons, New York, 2008.

    MATH  Google Scholar 

  23. Tang T L and Shieh S J, Long memory in stock index futures markets: A value-at-risk approach, Physica A: Statistical Mechanics and Its Applications, 2006, 366: 437–448.

    Article  Google Scholar 

  24. Caporin M, Evaluating value-at-risk measures in the presence of long memory conditional volatility, The Journal of Risk, 2008, 10(3): 79–110.

    Article  Google Scholar 

  25. Mcmillan D G and Kambouroudis D, Are riskmetrics forecasts good enough? Evidence from 31 stock markets, International Review of Financial Analysis, 2009, 18(3): 117–124.

    Article  Google Scholar 

  26. BCBS, Consultative document: Fundamental review of the trading book, Basel Committee on Banking Supervision, 2012.

  27. Perignon C and Smith D R, A new approach to comparing var estimation methods, The Journal of Derivatives, 2008, 16(2): 54–66.

    Article  Google Scholar 

  28. Candelon B, Colletaz G, Hurlin C, et al., Backtesting value-at-risk: A GMM duration-based test, Journal of Financial Econometrics, 2011, 9(2): 314–343.

    Article  Google Scholar 

  29. Kupiec P H, Techniques for verifying the accuracy of risk measurement models, The Journal of Derivatives, 1995, 3(2): 73–84.

    Article  Google Scholar 

  30. Christoffersen P F, Evaluating interval forecasts, International Economic Review, 1998, 39(4): 841–862.

    Article  MathSciNet  Google Scholar 

  31. Engle R F, A general approach to lagrange multiplier model diagnostics, Journal of Econometrics, 1982, 20(1): 83–104.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, 230026, China

    Keqi Tan, Yu Chen & Dan Chen

Authors
  1. Keqi Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Chen.

Ethics declarations

The authors declare no conflict of interest.

Additional information

The work was supported by the National Social Science Fund of China under Grant No. 22BTJ027.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tan, K., Chen, Y. & Chen, D. A New Risk Measure MMVaR: Properties and Empirical Research. J Syst Sci Complex 36, 2026–2045 (2023). https://doi.org/10.1007/s11424-023-2068-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-023-2068-1

Keywords

Search

Navigation