A computational study of a quasi-PORT methodology for VaR based on second-order reduced-bias estimation

Journal of Statistical Computation and Simulation

Volumn 82, Issue 4, 2012, Pages 587-602

  Figueiredo, Fernanda ^a   Gomes, M Ivette ^b   Henriques Rodrigues, Lígia ^c   Miranda, M Cristina ^d  

^a UNIVERSITY OF PORTO   (Portugal)

^b UNIVERSITY OF LISBON   (Portugal)

^c INSTITUTO POLITÉCNICO DE TOMAR   (Portugal)

^d UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

heuristics; semi parametric estimation; statistics of extremes; value at risk

Indexed keywords

EID: 84859598920     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949655.2010.547196     Document Type: Article

References (31)

1. Gnedenko, B. V. 1943. Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math., 44: 423-453.
2. Balkema, A. A. and de Haan, L. 1974. Residual life time at great age. Ann. Probab., 2: 792-804.
3. Pickands III, J. 1975. Statistical inference using extreme order statistics. Ann. Statist., 3: 119-131.
4. Embrechts, P., Klüppelberg, C. and Mikosch, T. 1997. Modelling Extremal Events for Insurance and Finance, Berlin, Heidelberg: Springer.
5. Reiss, R.-D. and Thomas, M. 2007. Statistical Analysis of Extreme Values, with Application to Insurance, Finance, Hydrology and Other Fields, 3, Basel: Birkhäuser Verlag.
6. Smith, R. L. 1987. Estimating tails of probability distributions. Ann. Statist., 15: 1174-1207.
7. Drees, H., Ferreira, A. and de Haan, L. 2004. On maximum likelihood estimation of the extreme value index. Ann. Appl. Probab., 14: 1179-1201.
8. Araújo Santos, P., Fraga Alves, M. I. and Gomes, M. I. 2006. Peaks over random threshold methodology for tail index and quantile estimation. Revstat, 4(3): 227-247.
9. Hill, B. 1975. A simple general approach to inference about the tail of a distribution. Ann. Statist., 3: 1163-1174.
10. Gomes, M. I., Fraga Alves, M. I. and Araújo Santos, P. 2008. PORT Hill and moment estimators for heavy-tailed models. Comm. Statist. Simulation Comput., 37: 1281-1306.
11. Caeiro, F., Gomes, M. I. and Pestana, D. D. 2005. Direct reduction of bias of the classical Hill estimator. Revstat, 3(2): 111-136.
12. Gomes, M. I. and Pestana, D. D. 2007. A sturdy reduced-bias extreme quantile (VaR) estimator. J. Amer. Statist. Assoc., 102(477): 280-292.
13. Gomes, M. I. and Pestana, D. D. 2007. A simple second order reduced-bias' tail index estimator. J. Stat. Comput. Simul., 77(6): 487-504.
14. Weissman, I. 1978. Estimation of parameters and large quantiles based on the k largest observations. J. Amer. Statist. Assoc., 73: 812-815.
15. Gomes, M. I. and Oliveira, O. 2001. The bootstrap methodology in statistics of extremes: Choice of the optimal sample fraction. Extremes, 4(4): 331-358.
16. Gomes, M. I., de Haan, L. and Henriques-Rodrigues, L. 2008b. Tail index estimation for heavy-tailed models: Accommodation of bias in weighted log-excesses. J. R. Stat. Soc. B, 70(1): 31-52.
17. Fraga Alves, M. I., Gomes, M. I. and de Haan, L. 2003. A new class of semi-parametric estimators of the second order parameter. Port. Math., 60(2): 194-213.
18. Gomes, M. I. and Martins, M. J. 2002. 'Asymptotically unbiased' estimators of the tail index based on external estimation of the second order parameter. Extremes, 5(1): 5-31.
19. Goegebeur, Y., Beirlant, J. and de Wet, T. 2008. Linking Pareto-tail kernel goodness-of-fit statistics with tail index at optimal threshold and second order estimation. Revstat, 6(1): 51-69.
20. Ciuperca, G. and Mercadier, C. 2010. Semi-parametric estimation for heavy tailed distributions. Extremes, 13(1): 55-87.
21. Goegebeur, Y., Beirlant, J. and de Wet, T. 2010. Kernel estimators for the second order parameter in extreme value statistics. J. Statist. Plann. Inference, 140(9): 2632-2652.
22. Caeiro, F., Gomes, M. I. and Henriques-Rodrigues, L. 2009. Reduced-bias tail index estimators under a third order framework. Comm. Statist. Theory Methods, 38(7): 1019-1040.
23. Caeiro, F. and Gomes, M. I. 2006. A new class of estimators of a 'scale' second order parameter. Extremes, 9(3-4): 193-211.
24. Gomes, M. I., Henriques-Rodrigues, L., Pereira, H. and Pestana, D. 2010. Tail index and second order parameters' semi-parametric estimation based on the log-excesses. J. Stat. Comput. Simul., 80(6): 653-666.
25. McNeil, A. and Frey, R. 2000. Estimation of tail-related risk measures for heteroscedastic financial times series: An extreme value approach. J. Empirical Finance, 7: 271-300.
26. Jones, M. C. and Faddy, M. J. 2003. A skew extension of the t-distribution, with applications. J. R. Stat. Soc. B, 65(1): 159-174.
27. McNeil, A., Frey, R. and Embrechts, P. 2005. Quantitative Risk Management: Concepts, Techniques and Tools, Princeton, NJ: Princeton University Press.
28. Holton, G. A. 2003. Value-at-Risk: Theory and Practice, San Diego, CA: Academic Press.
29. Drees, H. 2003. Extreme quantile estimation for dependent data, with applications to finance. Bernoulli, 9(4): 617-657.
30. Gomes, M. I., Hall, A. and Miranda, C. 2008. Subsampling techniques and the Jackknife methodology in the estimation of the extremal index. J. Comput. Statist. Data Anal., 52(4): 2022-2041.
31. Gomes, M. I. and Miranda, C. Proceedings of the ITI 2009. Finite sample behaviour of the mixed moment estimator in dependent frameworks, Edited by: Luzar-Stifler, V., Jarec, I. and Bekic, Z. pp.237-242. Zagreb: University of Zagreb Editions.