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Nonparametric estimation of Value-at-Risk

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Author Info

  • Ramon Alemany

    ()
    (Department of Econometrics, Riskcenter-IREA, University of Barcelona,Av. Diagonal, 690, 08034 Barcelona, Spain)

  • Catalina Bolancé

    ()
    (Department of Econometrics, Riskcenter-IREA, University of Barcelona,Av. Diagonal, 690, 08034 Barcelona, Spain)

  • Montserrat Guillén

    ()
    (Department of Econometrics, Riskcenter-IREA, University of Barcelona,Av. Diagonal, 690, 08034 Barcelona, Spain)

Abstract

A method to estimate an extreme quantile that requires no distributional assumptions is presented. The approach is based on transformed kernel estimation of the cumulative distribution function (cdf). The proposed method consists of a double transformation kernel estimation. We derive optimal bandwidth selection methods that have a direct expression for the smoothing parameter. The bandwidth can accommodate to the given quantile level. The procedure is useful for large data sets and improves quantile estimation compared to other methods in heavy tailed distributions. Implementation is straightforward and R programs are available.

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File URL: http://www.pcb.ub.edu/xreap/aplicacio/fitxers/XREAP2012-19.pdf
File Function: First version, 2012
Download Restriction: no

File URL: http://www.pcb.ub.edu/xreap/aplicacio/fitxers/XREAP2012-19.pdf
File Function: Revised version, 2012
Download Restriction: no

Bibliographic Info

Paper provided by Xarxa de Referència en Economia Aplicada (XREAP) in its series Working Papers with number XREAP2012-19.

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Length: 40 pages
Date of creation: Oct 2012
Date of revision: Oct 2012
Handle: RePEc:xrp:wpaper:xreap2012-19

Contact details of provider:
Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques i Empresarials, Universitat de Barcelona, c/ Tinent Coronel Valenzuela, 1-11, 08034 Barcelona
Phone: +34+934039653
Email:
Web page: http://www.pcb.ub.edu/xreap
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Related research

Keywords: kernel estimation; bandwidth selection; quantile; risk measures..;

This paper has been announced in the following NEP Reports:

References

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  1. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  2. Bolance, Catalina & Guillen, Montserrat & Perch Nielsen, Jens, 2000. "Kernel Density Estimation of Actuarial Loss Functions," Finance Working Papers 00-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  3. Bolancé, Catalina & Guillén, Montserrat & Nielsen, Jens Perch, 2008. "Inverse beta transformation in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1757-1764, September.
  4. Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
  5. Jean Pinquet & Guillén Montserrat & Catalina Bolancé, 2007. "On the link between credibility and frequency premium," Working Papers hal-00243063, HAL.
  6. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
  7. Vicente Royuela, 2012. "What about people in European Regional Science?," Working Papers XREAP2012-12, Xarxa de Referència en Economia Aplicada (XREAP), revised May 2012.
  8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  9. Guillen, Montserrat & Prieto, Faustino & Sarabia, José María, 2011. "Modelling losses and locating the tail with the Pareto Positive Stable distribution," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 454-461.
  10. Catalina Bolancé & Ramon Alemany & Montserrat Guillén, 2010. "Prediction of the economic cost of individual long-term care in the Spanish population," IREA Working Papers 201011, University of Barcelona, Research Institute of Applied Economics, revised Sep 2010.
  11. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
  12. Xosé-Luís Varela-Irimia, 2011. "Age effects, unobserved characteristics and hedonic price indexes: The Spanish car market in the 1990?s," Working Papers XREAP2011-11, Xarxa de Referència en Economia Aplicada (XREAP), revised Aug 2011.
  13. Marta Arespa, 2011. "Macroeconomics of extensive margins: a simple model," Working Papers XREAP2011-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Nov 2011.
  14. Daniel Albalate & Germà Bel, 2008. "Tourism and urban transport: Holding demand pressure under supply constraints," Working Papers XREAP2008-14, Xarxa de Referència en Economia Aplicada (XREAP), revised Dec 2008.
  15. David Pitt & Montserrat Guillén, 2010. "An introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions," Working Papers XREAP2010-03, Xarxa de Referència en Economia Aplicada (XREAP), revised Mar 2010.
  16. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
  17. Peng, Liang & Qi, Yongcheng & Wang, Ruodu & Yang, Jingping, 2012. "Jackknife empirical likelihood method for some risk measures and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 142-150.
  18. Marta Arespa, 2011. "A New Open Economy Macroeconomic Model with Endogenous Portfolio Diversifi cation and Firms Entry," Working Papers XREAP2011-15, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2011.
  19. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
  20. Montserrat Guillen & Jim Gustafsson & Jens Perch Nielsen & Paul Pritchard, 2007. "Using External Data in Operational Risk," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 32(2), pages 178-189, April.
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Citations

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Cited by:
  1. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.

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