Extreme Value Theory in Finance
II
Erik Brodin, Claudia Klüppelberg,
Claudia Klüppelberg
Munich University of Technology, Garching, Germany
Chalmers University of Technology, Göteborg, Sweden
Search for more papers by this authorErik Brodin, Claudia Klüppelberg,
Claudia Klüppelberg
Munich University of Technology, Garching, Germany
Chalmers University of Technology, Göteborg, Sweden
Search for more papers by this authorAbstract
Extreme value theory is a practical and useful tool for modeling and quantifying risk. In this article, after introducing basic concepts, we indicate how to apply it within a financial framework.
References
- 1 McNeil, A., Frey, R. & Embrechts, P. (2005). Quantitative Risk Management, Princeton University Press, Princeton.
- 2 P. Embrechts (ed) (2000). Extremes and Integrated Risk Management, UBS Warburg and Risk Books.
- 3 Rootzén, H. & Klüppelberg, C. (1999). A single number can't hedge against economic catastrophes, Ambio 28, 550–555.
- 4 Campbell, R.A. & Huisman, R. (2003). Measuring credit spread risk: incorporating the tails, Journal of Portfolio Management 29, 121–127.
- 5 Kuhn, G. (2004). Tails of credit default portfolios, Technical Report, Munich University of Technology, at http://www-m4.ma.tum.de/Papers/.
- 6
Lukas, A.,
Klaasen, P.,
Spreij, P. &
Straetmans, S.
(2003).
Tail behavior of credit loss distributions for general latent factor models,
Applied Mathematical Finance
10(4),
337–357.
10.1080/1350486032000160786 Google Scholar
- 7 Phoa, W. (1999). Estimating credit spread risk using extreme value theory, Journal of Portfolio Management 25, 69–73.
- 8 Böcker, K. & Klüppelberg, C. (2005). Operational VaR: a closed-form approximation, Risk 90–93.
- 9 Böcker, K. & Klüppelberg, C. (2006). Multivariate models for operational risk, Submitted for publication.
- 10 Chavez-Demoulin, V., Embrechts, P. & Nešlehová, J. (2005). Quantitative models for operational risk: extremes, dependence and aggregation, Journal of Banking and Finance 30(10), 2635–2658.
- 11 Moscadelli, M. (2004). The modelling of operational risk: experience with the analysis of the data collected by the Basel committee, Technical Report Number 517, Banca d'Italia.
- 12
Beirlant, J.,
Goegebeur, Y.,
Segers, J. &
Teugels, J.
(2004).
Statistics of Extremes: Theory and Applications,
John Wiley & Sons,
Chichester.
10.1002/0470012382 Google Scholar
- 13
Coles, S.G.
(2001).
An Introduction to Statistical Modeling of Extreme Values,
Springer,
London.
10.1007/978-1-4471-3675-0 Google Scholar
- 14
Embrechts, P.,
Klüppelberg, C. &
Mikosch, T.
(1997).
Modelling Extremal Events for Insurance and Finance,
Springer,
Berlin.
10.1007/978-3-642-33483-2 Google Scholar
- 15
Leadbetter, M.R.,
Lindgren, G. &
Rootzén, H.
(1983).
Extremes and Related Properties of Random Sequences and Processes,
Springer,
New York.
10.1007/978-1-4612-5449-2 Google Scholar
- 16 Reiss, R.-D. & Thomas, M. (2001). Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields, 2nd Edition, Birkhäuser, Basel.
- 17
Resnick, S.I.
(1987).
Extreme Values, Regular Variation and Point Processes,
Springer,
New York.
10.1007/978-0-387-75953-1 Google Scholar
- 18
Stephenson, A. &
Gilleland, E.
(2006).
Software for the analysis of extreme events: the current state and future directions,
Extremes
8(3),
87–109.
10.1007/s10687-006-7962-0 Google Scholar
- 19 Emmer, S., Klüppelberg, C. & Trüstedt, M. (1998). VaR–ein Maß für das extreme Risiko, Solutions 2, 53–63.
- 20 Smith, R.L. (1987). Estimating tails of the probability distributions, Annals of Statistics 15, 1174–1207.
- 21 Jorion, P. (2001). Value at Risk: The New Benchmark for Measuring Financial Risk, McGraw-Hill, New York.
- 22 Artzner, P., Delbaen, F., Eber, J.M. & Heath, D. (1999). Coherent measures of risk, Mathematical Finance 9, 203–228.
- 23 Föllmer, H. & Schied, A. (2002). Convex measures of risk and trading constraints, Finance and Stochastics 6(4), 429–447.
- 24 Drost, F.C. & Nijman, T.E. (1993). Temporal aggregation of GARCH processes, Econometrica 61, 909–927.
- 25 Fasen, V., Klüppelberg, C. & Lindner, A. (2006). Extremal behavior of stochastic volatility models, in Stochastic Finance, A.N. Shiryaev, M.d.R. Grossinho, P.E. Oliviera & M.L. Esquivel, eds, Springer, New York, pp. 107–155.
- 26 Klüppelberg, C. (2004). Risk management with extreme value theory, in Extreme Values in Finance, Telecommunication and the Environment, B. Finkenstädt & H. Rootzén, eds, Chapman & Hall/CRC, Boca Raton, pp. 101–168.
- 27 Ferro, T.A. & Segers, J. (2003). Inference for clusters of extreme values, Journal of the Royal Statistical Society, Series B 65, 545–556.
- 28
Laurini, F. &
Tawn, J.A.
(2003).
New estimators for the extremal index and other cluster characteristics,
Extremes
6(3),
189–211.
10.1023/B:EXTR.0000031179.49454.90 Google Scholar
- 29 Bollerslev, T., Engle, R.F. & Nelson, D. (1994). ARCH models, in Handbook of Econometrics, R. Engle & D. McFadden, eds, Elsevier, Amsterdam, Vol. IV, pp. 2959–3038.
- 30
McNeil, A. &
Frey, R.
(2000).
Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach,
Journal of Empirical Finance
7,
271–300.
10.1016/S0927-5398(00)00012-8 Google Scholar
- 31 Barndorff-Nielsen, O.E. & Shephard, N. (2001). Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion), Journal of the Royal Statistical Society, Series B 63, 167–241.
- 32 Klüppelberg, C., Lindner, A. & Maller, R. (2004). A continuous time GARCH process driven by a Lévy process: stationarity and second order behaviour, Journal of Applied Probability 41(3), 601–622.
- 33 Klüppelberg, C., Lindner, A. & Maller, R. (2006). Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models, in From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift, Y. Kabanov, R. Lipster & J. Stoyanov, eds, Springer, Berlin, pp. 393–419.
- 34
Beltratti, A. &
Morana, C.
(1999).
Computing value at risk with high frequency data,
Journal of Empirical Finance
6(5),
431–455.
10.1016/S0927-5398(99)00008-0 Google Scholar
- 35
Dacorogna, M.,
Müller, U.,
Pictet, O. &
de Vries, C.
(2001).
Extremal forex returns in extremely large data sets,
Extremes
4(2),
105–127.
10.1023/A:1013917009089 Google Scholar
- 36 Mikosch, T. (2005). How to model multivariate extremes if one must? Statistica Neerlandica 59(3), 324–338.
- 37 Resnick, S.I. (2007). Heavy Tail Phenomena: Probabilistic and Statistical Modeling, Springer, New York.
- 38 Klüppelberg, C. & Resnick, S.I. (2008). The Pareto copula, aggregation of risks and the Emperor's socks, Journal of Applied Probability 45(1), To appear.
- 39
Hauksson, H.,
Dacorogna, M.,
Domenig, T.,
Müller, U. &
Samorodnitsky, G.
(2001).
Multivariate extremes, aggregation and risk estimation,
Quantitative Finance
1(1),
79–95.
10.1080/713665553 Google Scholar
- 40
Stărică, C.
(1999).
Multivariate extremes for models with constant conditional correlations,
Journal of Empirical Finance
6,
515–553.
10.1016/S0927-5398(99)00018-3 Google Scholar
- 41
Hsing, T.,
Klüppelberg, C. &
Kuhn, G.
(2004).
Dependence estimation and visualization in multivariate extremes with applications to financial data,
Extremes
7,
99–121.
10.1007/s10687-005-6194-z Google Scholar
- 42 Einmahl, J., de Haan, L. & Piterbarg, V.I. (2001). Nonparametric estimation of the spectral measure of an extreme value distribution, Annals of Statistics 29, 1401–1423.
- 43 Klüppelberg, C., Kuhn, G. & Peng, L. (2007). Semi-parametric models for the multivariate tail dependence function, Under revision for Scandinavian Journal of Statistics, To appear.
- 44 Klüppelberg, C., Kuhn, G. & Peng, L. (2007). Estimating the tail dependence of an elliptical distribution, Bernouli 13(1), 229–251.
- 45 Brodin, E. & Klüppelberg, C. (2006). Modeling, Estimation and Visualization of Multivariate Dependence for High-Frequency Data, Munich University of Technology, at http://www.ma.tum.de/stat/, Preprint.
- 46 Rootzén, H. & Taijvidi, N. (2006). Multivariate generalized Pareto distribution, Bernoulli 12(5), 917–930.
Citing Literature
Encyclopedia of Quantitative Risk Analysis and Assessment
Browse other articles of this reference work:
