Suarez, R (2001): Improving Modeling of Extreme Events using Generalized Extreme Value Distribution or Generalized Pareto Distribution with Mixing Unconditional Disturbances.

PDF
MPRA_paper_17443.pdf Download (2MB)  Preview 
Abstract
In this paper an alternative nonparametric historical simulation approach, the Mixing Unconditional Disturbances model with constant volatility, where price paths are generated by reshuffling disturbances for S&P 500 Index returns over the period 1950  1998, is used to estimate a Generalized Extreme Value Distribution and a Generalized Pareto Distribution. An ordinary backtesting for period 1999  2008 was made to verify this technique, providing higher accuracy returns level under upper bound of the confidence interval for the Block Maxima and the PeakOver Threshold approaches with Mixing Unconditional Disturbances. This method can be an effective tool to create value for stresstesting valuation.
Item Type:  MPRA Paper 

Original Title:  Improving Modeling of Extreme Events using Generalized Extreme Value Distribution or Generalized Pareto Distribution with Mixing Unconditional Disturbances 
Language:  English 
Keywords:  Extreme Value, Block Maxima, Peak Over Threshold, Mixing Unconditional Disturbances 
Subjects:  C  Mathematical and Quantitative Methods > C0  General 
Item ID:  17443 
Depositing User:  Ronny Suarez 
Date Deposited:  22. Sep 2009 10:28 
Last Modified:  19. Feb 2013 00:04 
References:  Aragones, J.R., Blanco, C., Dowd, K. (2001) Incorporating Stress Tests into Market Risk Modeling. Derivatives Quarterly: 4449. Bensalah, Y. (2000). Steps in Applying Extreme Value Theory to Finance: A Review. Working Paper No. 200020. Bank of Canada. Castillo, E., Hadi, A. S., Balakrishnan, N., and Sarabia, J. M. (2005). Extreme Value and Related Models with Applications in Engineering and Science. John Wiley & Sons Inc., New Jersey. Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer, London. Embrechts, P., Resnick, S., Samorodnitsky, G. (1999). Extreme Value Theory as a Risk Management Tool. North American Actuarial Journal: 3, 3041. Embrechts, P. (2000). Extreme Value Theory: Potential and Limitations as an Integrated Risk Management Tool. Derivatives Use, Trading & Regulation: 6, 449456. Diebold, F.X., Schuermann, T., and Stroughair, J.D. (1998). Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management. Financial Institution Center, Wharton. Gilli, M., and Kellezi, E. (2006). An Application to Extreme Value Theory for Measuring Risk. Computational Economics: 27(1), 123. Habiboellah, N. (2005). The Application of Extreme Value Theory in Banking. Business Mathematics & Informatics. Universiteit Amsterdam. McNeil, A. J. (1999). Extreme Value Theory for Risk Managers. Internal Modelling and CAD II. RISK Books, 93113. Rootzen, H. and Kluppelberg, C. (1999). A single number can't hedge against economic catastrophes. Ambio: 28, 550555. Reiss, R. D., and Thomas, M. (2007). Statistical Analysis of Extreme Values: From Insurance, Finance, Hydrology and Other Fields. 3ed. Edition. Birkhauser, Basel. Schachter, B. (1998): The Value of Stress Testing in Market Risk Management. Derivatives Risk Management Service. Tompkins, R. G., and D'Ecclesia, R. L. (2006). Unconditional Return Disturbances: A Nonparametric Simulation Approach. Journal of Banking & Finance: 30(1), 287314. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/17443 