Classification of methods for risk measures VaR and CVaR calculation and estimation

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2016.3.11

Keywords:

estimation, Value-at-Risk, Conditional Value-at-Risk, structural-hierarchical scheme, systematization, classification

Abstract

A systematic classification of the existing approaches for popular risk measures VaR and CVaR calculating and estimating is fulfilled. A review of the most used methods is done. For convenience, the considered methods are reduced to common econometric designations and concepts, guidance on the use of the methods is proposed. The correctness of the considered methods is numerically confirmed.

Author Biographies

Nataliia G. Zrazhevska, Educational-Scientific Complex "Institute for Applied System Analysis" NTUU "KPI", Kyiv, Ukraine

Nataliia Zrazhevska,

postgraduate at Educational-Scientific Complex "Institute for Applied System Analysis" NTUU "KPI", Kyiv, Ukraine

Nataliia

A. G. Zrazhevsky, Head of Analytical Department at American Optimal Decision, Florida, USA

Oleksii Zrazhevskyi,

Ph.D. in Technical Sciences, Head of Analytical Department at American Optimal Decision, Florida, USA

References

RiskMetrics. Technical Document, 4-th Edition / J.P. Morgan, December 1996. — 296 p.

Dowd K. Measuring Market Risk / K. Dowd // Chichester: John Wiley & Sons, Inc., 2005. — 410 p.

Tsay R.S. Analysis of Financial Time Series / R.S. Tsay. — Hoboken: John Wiley & Sons, Inc., 2010. — 714 p.

Embrechts P. Correlation and dependence in risk management: properties and pitfalls. Risk Management: Value at Risk and Beyond / P. Embrechts, A.J. McNeil, D. Straumann // Cambridge: Cambridge University Press, 2002. — P.176–223.

Artzner P. Coherent measures of risk / P. Artzner, F. Delbaen, J.M. Eber, D. Heath // Mathematical Finance. — 1999. — № 9. — P. 203–228.

Rockafellar R.T. Optimization of conditional value-at-risk / R.T. Rockafellar, S.P. Uryasev // Journal of Risk. — 2000. — 2. — P. 21–42.

Nadarajah S. Estimation methods for expected shortfall / S. Nadarajah, Zhang Bo, S. Chan // Quantitative Finance. — 2014. — 14. — P. 271–291.

Yamai Y. Comparative analysis of expected shortfall and value-at-risk: their estimation error, decomposition and optimization / Y. Yamai, T. Yoshiba // Monetary and Economic Studies. — 2002. — 20(1). — P. 57–86.

Sarykalin S. VaR vs.CVaR / S. Sarykalin, G. Serraino, S. Uryasev // Risk Management and Optimization Tutorialsin Operations Research INFORMS. — 2008. — P. 270–294.

Zhurovs'kyj M.Z. Osnovy systemnoho analizu / M.Z. Zhurovs'kyj, N.D. Pankratova. — K.: BHV, 2007. — 544 s.

Acerbi C. Expected Shortfall: a natural coherent alternative to Value at Risk / C. Acerbi, D. Tasche // Economic Notes. — 2002. — 31. — P. 379–388.

Chen S.X. Nonparametric estimation of expected shortfall / S.X. Chen // Journal of Financial Econometrics. — 2008. — 6. — P. 87–107.

Peracchi F. On estimating the conditional expected shortfall / F. Peracchi, A.V. Tanase // Applied Stochastic Models in Business and Industry. — 2008. — 24. — P. 471–493.

Inui K. On the significance of expected shortfall as a coherent risk measure / K. Inui, M. Kijima // Journal of Banking and Finance. — 2005. — 29. — P. 853–864.

Men'shikov I.S. Rynochnye riski, modeli i metody / I.S. Men'shikov, D.A. Shelagin. — M.: Ross. akademija nauk. Vychislit. tsentr, 2006. — 55 s.

Rockafellar R.T. Conditional value-at-risk for general loss distributions / R.T. Rockafellar, S.P. Uryasev // Journal of Banking & Finance. — 2002. — 26. — P. 1443–1471.

Kjellson B. Forecasting Expected Shortfall / B. Kjellson // Bachelor’s Theses in Mathematical Sciences. — 2013. — K7. — P. 1–39.

Bernardi M. Risk measures for skew normal mixtures // Statistics & Probability Letters. – 2013. — 83 (8). — P. 1819–1824.

Broda S.A. Expected shortfall for distributions in finance / S.A. Broda, M.S. Paolella // Statistical Tools for Finance and Insurance. — 2011. — P. 57–99.

Zivot E. Modeling Financial Time Series with S-PLUS / E. Zivot, J. Wang. — New York: Springer-Verlag, 2003. — 705 p.

Danielsson J. Value at Risk and Extreme Returns / J. Danielsson, C.G. de Vries // Annales d'economie et de Statistique. — 2000. — 60. — P. 236–269.

Embrechts P. Strategic long-term financial risks: single risk factors / P. Embrechts, R. Kaufmann, P. Patie // Computational Optimization and Applications. — 2005. — 32. — P. 61–90.

Ou S. Robustness analysis and algorithm of expected shortfall based on extreme-value block minimum model / S. Ou, D. Yi // Proceedings of the 2009 International Conference. — 2009.

Rinker J. Peak-over-Threshold Method for Extreme Values / J. Rinker // Duke University. — 2013. — 22. — P. 1–6.

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Published

2016-09-26

Issue

Section

Mathematical methods, models, problems and technologies for complex systems research