Quantile estimation for the generalized pareto distribution with application to finance
DOI:
https://doi.org/10.2298/YJOR110308013JKeywords:
generalized Pareto distributions, excesses over high thresholds, quantiles of the distribution, Value at RiskAbstract
Generalized Pareto distributions (GPD) are widely used for modeling excesses over high thresholds (within the framework of the POT-approach to modeling extremes). The aim of the paper is to give the review of the classical techniques for estimating GPD quantiles, and to apply these methods in finance - to estimate the Value-at-Risk (VaR) parameter, and discuss certain difficulties related to this subject.References
Ashkar, F., and Tatsambon, C.N., “Revisiting some estimation methods for the generalized Pareto distribution”, Journal of Hydrology, 346 (2007) 136-143.
Balkema, A., and de Haan, L., “Residual life time at great age”, Annals of Probability, 2 (1974) 792-804.
Castillo, E., and Hadi, A.S., “Fitting the generalized Pareto distribution to data”, Journal of the American Statistical Association, 92 (440) (1997) 1609-1620.
Connolly, R.A., “An examination of the robustness of the weekend effect”, Journal of Financial and Quantitative Analysis, 24 (2) (1989) 133-169.
Davison, A.C., and Smith, R.L., “Models for exceedances over high thresholds”, Journal of the Royal Statistical Society, B 52 (3) (1990) 393-442.
del Castillo, J., and Daoudi, J., “Estimation of the generalized Pareto distribution”, Statistics and Probability Letters, 79 (2009) 684-688.
de Zea Bermudez, P., and Kotz, S., “Parameter estimation of the generalized Pareto distribution – Parts I and II”, Journal of Statistical Planning and Inference, 140 (2010) 1353-1388.
Embrechts, P., Kluppelberg, C., and Mikosch, T., Modelling Extremal Events, 4th edition, Springer, Verlag, Berlin, 2003.
French, K.R., “Stock returns and the weekend effect”, Journal of Financial Economics, 8 (1980) 55-69.
Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, R. “Probability weighted moments: definition and relation to parameters of several distributions, expressible in inverse form”, Water Resources Research, 15 (5) (1979) 1049-1054.
Hosking, J.R.M., and Wallis, J.R., “Parameter and quantile estimation for the generalized Pareto distribution”, Technometrics, 29 (3) (1987) 339-349.
Jocković, J., and Mladenović, P., “Coupon collector’s problem and generalized Pareto distributions”, Journal of Statistical Planning and Inference, 141 (2011) 2348–2352.
Juárez, S.F., and Schucany, W.R., “Robust and efficient estimation for the generalized Pareto distribution”, EXTREMES, 7 (2004) 237-251.
Katz, R.W., Brush, G.S., and Parlange, M.B., “Statistics of extremes: Modeling ecological disturbances”, Ecology, 86 (5) (2005) 1124-1134.
Keim, D. and Stambaugh, R., “A further investigation of the weekend effect in stock returns”, Journal of Finance, 39 (1984) 819-35.
Kyselý, J., Picek, J., and Beranová, R., “Estimating extremes in climate change simulations using the peaks-over-threshold method with a non-stationary threshold”, Global and Planetary Change, 72 (2010) 55–68.
Mackay, E.B.L., and Challenor, P.G., “A comparison of estimators for the generalized Pareto distribution”, Ocean Engineering, 38 (2011) 1338-1346.
Mladenović, Z., and Mladenović, P., “Praktični problemi ocene rizika u analizi dnevnih vremenskih serija”, Zbornik SYM-OP-IS 2007, 2007, 117-120.
Peng, L., and Welsh, A.H., “Robust estimation of the generalized Pareto distribution”, EXTREMES, 4 (1) (2001) 53-65.
Pickands, J., “Statistical inference using extreme order statistics”, The Annals of Statistics, 3 (1975) 119-131.
Reiss, R.-D., and Thomas, M., Statistical Analysis of Extreme Values From Insurance, Finance, Hydrology and Other Fields, Birkhauser Basel, 2001.
Ulussever, T., Guran Yumusak, I., and Kar, M, “The Day of the week effect in the Saudi stock exchange: a non linear Garch analysis”, Journal of Economic and Social Studies, 1 (1) (2011) 10-23.
Downloads
Published
Issue
Section
License
Copyright (c) 2012 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.