An Application of Extreme Value Theory for Measuring Financial Risk in the Uruguayan Pension Fund
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Publicado
abr 29, 2017
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Resumen
Traditional methods for financial risk measures adopts normal distributions as a pattern of the financial return behavior. Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. In this paper, we use Peaks Over Threshold (POT) model of Extreme Value Theory (EVT), and General Pareto Distribution (GPD) which can give a more accurate description on tail distribution of financial losses. The EVT and POT techniques provides well established statistical models for the computation of extreme risk measures like the Return Level, Value at Risk and Expected Shortfall. In this paper we apply this technique to a series of daily losses of AFAP SURA over an 18-year period (1997-2015), AFAP SURA is the second largest pension fund in Uruguay with more than 310,000 clients and assets under management over USD 2 billion. Our major conclusion is that the POT model can be useful for assessing the size of extreme events. VaR approaches based on the assumption of normal distribution are definitely overestimating low percentiles (due to the high variance estimation), and underestimate high percentiles (due to heavy tails). The absence of extreme values in the assumption of normal distribution underestimate the Expected Shortfall estimation for high percentiles. Instead, the extreme value approach on POT model seems coherent with respect to the actual losses observed and is easy to implement.
Palabras clave
Extreme Value Theory; General Pareto Distribution; Peaks Over Threshold; Risk Measures; Value at Risk; Pension Fund
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Citas
[1] Artzner, P.; Delbaen, F.; Eber, J. M.; Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance 9 (3): 203.
[2] Balkema, A., and de Haan, L. (1974). Residual life time at great age, Annals of Probability, 2, 792-804.
[3] Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London
[4] Dowd, K. (2002) Measuring Market Risk. John Wiley & Sons.
[5] Embrechts, P. (1999). Extreme Value Theory as a Risk Management Tool. North American Actuarial Journal, 3(2).
[6] Embrechts P., Kluppelberg C. and Mikosch T. (1997) Modelling extremal events: for insurance and finance, Springer, Berlin.
[7] Fisher, R.A.; Tippett, L.H.C. (1928). Limiting forms of the frequency distribution of the largest and smallest member of a sample, Proc. Cambridge Phil. Soc. 24: 180-190.
[8] Gilli, M., Kellezi, E. (2006). An application of extreme value theory for measuring financial risk. Computational Economics 27, 207-228.
[9] Gnedenko, B. V. (1948). On a local limit theorem of the theory of probability, Uspekhi Mat. Nauk, 3:3(25), 187-194.
[10] Makarov, M. (2007) Applications of exact extreme value theorem. Journal of Operational Risk, Volume 2, number 1 pages 115-120.
[11] McNeil A.J., Frey R. and Embrechts P. (2005) Quantitative risk management: Concepts, techniques and tools. Princeton University Press.
[12] Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3, 119-131.
[13] Reiss, R.-D. and Thomas, M. (2007). Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields, Third Edition. Birkhauser, Basel.
[14] Resnick, S. I. (1987) Extreme Values, Regular Variation, and Point Processes, Springer.
[15] Rockafellar, R.T.; Uryasev S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, Volume 26, Issue 7, Pages 1443-1471.
[2] Balkema, A., and de Haan, L. (1974). Residual life time at great age, Annals of Probability, 2, 792-804.
[3] Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London
[4] Dowd, K. (2002) Measuring Market Risk. John Wiley & Sons.
[5] Embrechts, P. (1999). Extreme Value Theory as a Risk Management Tool. North American Actuarial Journal, 3(2).
[6] Embrechts P., Kluppelberg C. and Mikosch T. (1997) Modelling extremal events: for insurance and finance, Springer, Berlin.
[7] Fisher, R.A.; Tippett, L.H.C. (1928). Limiting forms of the frequency distribution of the largest and smallest member of a sample, Proc. Cambridge Phil. Soc. 24: 180-190.
[8] Gilli, M., Kellezi, E. (2006). An application of extreme value theory for measuring financial risk. Computational Economics 27, 207-228.
[9] Gnedenko, B. V. (1948). On a local limit theorem of the theory of probability, Uspekhi Mat. Nauk, 3:3(25), 187-194.
[10] Makarov, M. (2007) Applications of exact extreme value theorem. Journal of Operational Risk, Volume 2, number 1 pages 115-120.
[11] McNeil A.J., Frey R. and Embrechts P. (2005) Quantitative risk management: Concepts, techniques and tools. Princeton University Press.
[12] Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3, 119-131.
[13] Reiss, R.-D. and Thomas, M. (2007). Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields, Third Edition. Birkhauser, Basel.
[14] Resnick, S. I. (1987) Extreme Values, Regular Variation, and Point Processes, Springer.
[15] Rockafellar, R.T.; Uryasev S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, Volume 26, Issue 7, Pages 1443-1471.