Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
How Computational Statistics Became the Backbone of Modern Data Science Kapitel lesen Erstes Kapitel lesen

2012 | OriginalPaper | Buchkapitel

34. Heavy-Tailed Distributions in VaR Calculations

verfasst von : Adam Misiorek, Rafał Weron

Erschienen in: Handbook of Computational Statistics

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Market risks are the prospect of financial losses – or gains – due to unexpected changes in market prices and rates. Evaluating the exposure to such risks is nowadays of primary concern to risk managers in financial and non-financial institutions alike. Since the early 1990s a commonly used market risk estimation methodology has been the Value at Risk (VaR).

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Bagging, Boosting and Ensemble Methods
Nächstes Kapitel Econometrics
Literatur
Alexander, C.: Market Risk Analysis, Wiley, Chichester (2008)
Atkinson, A.C.: The simulation of generalized inverse Gaussian and hyperbolic random variables. SIAM J. Sci. Stat. Comput. 3, 502–515 (1982)MATHCrossRef
Barndorff-Nielsen, O.E.: Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond. A 353, 401–419 (1977)CrossRef
Barndorff-Nielsen, O.E.: Normal ∖ ∖ Inverse Gaussian Processes and the Modelling of Stock Returns, Research Report 300, Department of Theoretical Statistics, University of Aarhus (1995)
Barndorff-Nielsen, O.E., Blaesild, P.: Hyperbolic distributions and ramifications: Contributions to theory and applications. In: Taillie, C., Patil, G., Baldessari, B. (eds.) Statistical Distributions in Scientific Work, vol. 4, pp.19–44. Reidel, Dordrecht (1981)CrossRef
Barone-Adesi, G., Giannopoulos, K., Vosper, L.: VaR without correlations for portfolios of derivative securities. J. Futures Market. 19(5), 583–602 (1999)CrossRef
Bianchi, M.L., Rachev, S.T., Kim, Y.S., Fabozzi, F.J.: Tempered stable distributions and processes in finance: Numerical analysis. In: Corazza, M., Claudio, P.P. (eds.) Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer, New York (2010)
Bibby, B.M., Sørensen, M.: Hyperbolic processes in finance, In: Rachev, S.T. (eds.) Handbook of Heavy-tailed Distributions in Finance, North Holland, NY, USA (2003)
Blaesild, P., Sorensen, M.: HYP – a Computer Program for Analyzing Data by Means of the Hyperbolic Distribution, Research Report 248, Department of Theoretical Statistics, Aarhus University (1992)
Boyarchenko, S.I., Levendorskii, S.Z.: Option pricing for truncated Lévy processes. Int. J. Theor. Appl. Fin. 3, 549–552 (2000)MATHCrossRef
Brcich, R.F., Iskander, D.R., Zoubir, A.M.: The stability test for symmetric alpha stable distributions. IEEE Trans. Signal Process. 53, 977–986 (2005)MathSciNetCrossRef
Carr, P., Geman, H., Madan, D.B., Yor, M.: The fine structure of asset returns: An empirical investigation, J. Bus. 75, 305–332 (2002)CrossRef
Chambers, J.M., Mallows, C.L., Stuck, B.W.: A Method for Simulating Stable Random Variables. J. Am. Stat. Assoc. 71, 340–344 (1976)MathSciNetMATHCrossRef
Chen, Y., Härdle, W., Jeong, S.-O.: Nonparametric risk management with generalized hyperbolic distributions. J. Am. Stat. Assoc. 103, 910–923 (2008)MATHCrossRef
Cizek, P., Härdle, W., Weron, R.: Statistical Tools for Finance and Insurance, 2nd edition, Springer, Berlin (2011)MATHCrossRef
Cont, R., Potters, M., Bouchaud, J.-P.: Scaling in stock market data: Stable laws and beyond, In: Dubrulle, B., Graner, F., Sornette, D. (eds.) Scale Invariance and Beyond, Proceedings of the CNRS Workshop on Scale Invariance, Springer, Berlin (1997)CrossRef
D’Agostino, R.B., Stephens, M.A.: Goodness-of-Fit Techniques, Marcel Dekker, New York (1986)
Dagpunar, J.S.: An easily implemented generalized inverse gaussian generator. Comm. Stat. Simul. 18, 703–710 (1989)MathSciNetCrossRef
Danielsson, J., Hartmann, P., De Vries, C.G.: The cost of conservatism: Extreme returns, value at risk and the Basle multiplication factor. Risk 11, 101–103 (1998)
Dominicy, Y., Veredas, D.: The Method of Simulated Quantiles, ECARES working paper, pp. 2010–008 (2010)
DuMouchel, W.H.: Stable Distributions in Statistical Inference, Ph.D. Thesis, Department of Statistics, Yale University (1971)
DuMouchel, W.H.: On the asymptotic normality of the maximum–likelihood estimate when sampling from a stable distribution. Ann. Stat. 1(5), 948–957 (1973)MathSciNetMATHCrossRef
Eberlein, E., Keller, U.: Hyperbolic distributions in finance. Bernoulli 1, 281–299 (1995)MATH
Eberlein, E., Keller, U., Prause, K.: New insights into the smile, mispricing and Value at Risk: The hyperbolic model, J. Bus. 71, 371–406 (1998)CrossRef
Fama, E.F., Roll, R.: Parameter estimates for symmetric stable distributions. J. Am. Stat. Assoc. 66, 331–338 (1971)MATHCrossRef
Fan, Z.: arameter estimation of stable distributions. Comm. Stat. Theor. Meth. 35(2), 245–255 (2006)MATHCrossRef
Fang, K.-T., Kotz, S., Ng, K.-W.: Symmetric Multivariate and Related Distributions, Chapman & Hall, London (1987)
Franke, J., Härdle, W., Hafner, Ch.: Statistics of Financial Markets, 2nd ed., Springer, Berlin (2008)MATH
Fragiadakis, K., Karlis, D., Meintanis, S.G.: Tests of fit for normal inverse Gaussian distributions. Stat. Meth. 6, 553–564 (2009)MathSciNetMATHCrossRef
Fusai, G., Roncoroni, A.: Implementing Models in Quantitative Finance: Methods and Cases, Springer, New York (2008)MATH
Garcia, R., Renault, E., Veredas, D.: Estimation of stable distributions by indirect inference, Journal of Econometrics 161(2), 325–337 (2011)MathSciNetCrossRef
Grabchak, M.: Maximum likelihood estimation of parametric tempered stable distributions on the real line with applications to finance, Ph.D. thesis, Cornell University (2010)
Grabchak, M., Samorodnitsky, G.: Do financial returns have finite or infinite variance? A paradox and an explanation. Quantitative Finance 10(8), 883–893 (2010)MathSciNetMATHCrossRef
Guillaume, D.M., Dacorogna, M.M., Dave, R.R., Müller, U.A., Olsen, R.B., Pictet, O.V.: From the birds eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets. Fin. Stoch. 1, 95–129 (1997)MATHCrossRef
Holt, D.R., Crow, E.L.: Tables and graphs of the stable probability density functions. J. Res. Natl. Bur. Stand. B 77B, 143–198 (1973)MathSciNet
Janicki, A., Kokoszka, P.: Computer investigation of the rate of convergence of LePage type series to alpha-stable random variables. Statistica 23, 365–373 (1992)MathSciNetMATH
Janicki, A., Weron, A.: Simulation and Chaotic Behavior of α-Stable Stochastic Processes, Marcel Dekker (1994b)
Joe, H.: Multivariate Models and Dependence Concepts, Chapman & Hall, London (1997)MATH
Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk, (3rd edn.), McGraw-Hill, NY, USA (2006)
Karlis, D.: An EM type algorithm for maximum likelihood estimation for the Normal Inverse Gaussian distribution. Stat. Probab. Lett. 57, 43–52 (2002)MathSciNetMATHCrossRef
Karlis, D., Lillestöl, J.: Bayesian estimation of NIG models via Markov chain Monte Carlo methods. Appl. Stoch. Models Bus. Ind. 20(4), 323–338 (2004)MathSciNetMATHCrossRef
Kawai, R., Masuda, H.: On simulation of tempered stable random variates, Journal of Computational and Applied Mathematics 235(8), 2873-2887 (2011)MathSciNetMATHCrossRef
Kogon, S.M., Williams, D.B.: Characteristic function based estimation of stable parameters, In: Adler, R., Feldman, R., Taqqu, M. (eds.) A Practical Guide to Heavy Tails, pp. 311–335 Birkhauser, Basel (Boston/Stuttgart) (1998)
Koponen, I.: Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process. Phys. Rev. E 52, 1197–1199 (1995)CrossRef
Kuester, K., Mittnik, S., Paolella, M.S.: Value-at-Risk prediction: A comparison of alternative strategies. J. Fin. Econometrics 4(1), 53–89 (2006)CrossRef
Küchler, U., Neumann, K., Sørensen, M., Streller, A.: Stock returns and hyperbolic distributions. Math. Comput. Modell. 29, 1–15 (1999)MATHCrossRef
Lévy, P.: Calcul des Probabilites, Gauthier Villars (1925)
Lombardi, M.J.: Bayesian inference for α-stable distributions: A random walk MCMC approach. Comput. Stat. Data Anal. 51(5), 2688–2700 (2007)MathSciNetMATHCrossRef
Madan, D.B., Seneta, E.: The variance gamma (V.G.) model for share market returns. J. Bus. 63, 511–524 (1990)
Mandelbrot, B.B.: The variation of certain speculative prices. J. Bus. 36, 394–419 (1963)CrossRef
Mantegna, R.N.: Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes. Phy. Rev. E 49, 4677–4683 (1994)CrossRef
Mantegna, R.N., Stanley, H.E.: Stochastic processes with ultraslow convergence to a Gaussian: The truncated Lévy flight. Phys. Rev. Lett. 73, 2946–2949 (1994)MathSciNetMATHCrossRef
Matacz, A.: Financial modeling and option theory with the truncated lévy process. Int. J. Theor. Appl. Fin. 3(1), 143–160 (2000)MathSciNetMATHCrossRef
Matsui, M., Takemura, A.: ’Some improvements in numerical evaluation of symmetric stable density and its derivatives. Comm. Stat. Theor. Meth. 35(1), 149–172 (2006)MathSciNetMATHCrossRef
Matsui, M., Takemura, A.: Goodness-of-fit tests for symmetric stable distributions – empirical characteristic function approach. TEST 17(3), 546–566 (2008)MathSciNetMATHCrossRef
McNeil, A.J., Rüdiger, F., Embrechts, P.: Quantitative Risk Management, Princeton University Press, Princeton, NJ (2005)
Michael, J.R., Schucany, W.R., Haas, R.W.: Generating random variates using transformations with multiple roots. Am. Stat. 30, 88–90 (1976)MATH
Mittnik, S., Doganoglu, T., Chenyao, D.: Computing the Probability Density Function of the Stable Paretian Distribution. Math. Comput. Modell. 29, 235–240 (1999)MathSciNetMATHCrossRef
Mittnik, S., Paolella, M.S.: A simple estimator for the characteristic exponent of the stable Paretian distribution. Math. Comput. Modell. 29, 161–176 (1999)MathSciNetMATHCrossRef
Mittnik, S., Rachev, S.T., Doganoglu, T., Chenyao, D.: Maximum likelihood estimation of stable paretian models. Math. Comput. Modell. 29, 275–293 (1999)MathSciNetMATHCrossRef
Nelsen, R.B.: An Introduction to Copulas, Springer, New York (1999)MATH
Nolan, J.P.: Numerical calculation of stable densities and distribution functions. Comm. Stat. Stoch. Model. 13, 759–774 (1997)MathSciNetMATHCrossRef
Nolan, J.P.: An Algorithm for Evaluating Stable Densities in Zolotarev’s (M) Parametrization. Math. Comput. Modell. 29, 229–233 (1999)MATHCrossRef
Nolan, J.P.: Maximum Likelihood Estimation and Diagnostics for Stable Distributions. In: Barndorff-Nielsen, O.E., Mikosch, T., Resnick, S. (eds.) Lévy Processes, Brikhäuser, Boston (2001)
Nolan, J.P.: Stable Distributions – Models for Heavy Tailed Data, Birkhäuser, Boston (2012); In progress, Chapter 1 online at academic2.american.edu/ ∼ jpnolan.
Ojeda, D.: Comparison of stable estimators, Ph.D. Thesis, Department of Mathematics and Statistics, American University (2001)
Paolella, M.S.: Intermediate Probability: A Computational Approach, Wiley, Chichester (2007)MATH
Peters, G.W., Sisson, S.A., Fan, Y.: Likelihood-free Bayesian inference for α-stable models, Computational Statistics & Data Analysis, forthcoming (2011)
Poirot, J., Tankov, P.: Monte Carlo option pricing for tempered stable (CGMY) processes. Asia. Pac. Financ. Market. 13(4), 327-344 (2006)MATHCrossRef
Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C, Cambridge University Press (1992); See also: http://​www.​nr.​com.
Protassov, R.S.: EM-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with fixed λ. Stat. Comput. 14, 67–77 (2004)MathSciNetCrossRef
Rachev, S., Mittnik, S.: Stable Paretian Models in Finance, Wiley, New York (2000)
Samorodnitsky, G., Taqqu, M.S.: Stable Non–Gaussian Random Processes, Chapman & Hall, London (1994)MATH
Stahl, G.: Three cheers. Risk 10, 67–69 (1997)
Stute, W., Manteiga, W.G., Quindimil, M.P.: Bootstrap based goodness-of-fit-tests. Metrika 40, 243–256 (1993)MATH
Trivedi, P.K., Zimmer, D.M.: Copula modeling: An introduction for practitioners. Foundations Trend. Econometrics 1(1), 1–111 (2005)MathSciNetMATHCrossRef
Venter, J.H., de Jongh, P.J.: Risk estimation using the Normal Inverse Gaussian distribution. J. Risk 4, 1–23 (2002)
Weron, R.: On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables, Stat. Probab. Lett. 28, 165–171 (1996); See also R. Weron (1996) Correction to: On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables, Working Paper, Available at MPRA: http://​mpra.​ub.​uni-muenchen.​de/​20761/​.
Weron, R.: Levy–Stable distributions revisited: Tail index > 2 does not exclude the Levy–Stable regime. Int. J. Modern Phys. C 12, 209–223 (2001)CrossRef
Weron, R.: Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach, Wiley, Chichester (2006)
Zolotarev, V.M.: On representation of stable laws by integrals. Selected Trans. Math. Stat. Probab. 4, 84–88 (1964)MathSciNet
Zolotarev, V.M.: One–Dimensional Stable Distributions, American Mathematical Society (1986)
Metadaten
Titel
Heavy-Tailed Distributions in VaR Calculations
verfasst von
Adam Misiorek
Rafał Weron
Copyright-Jahr
2012
Verlag
Springer Berlin Heidelberg
Buch
Handbook of Computational Statistics

Print ISBN: 978-3-642-21550-6

Electronic ISBN: 978-3-642-21551-3

Copyright-Jahr: 2012

DOI
https://doi.org/10.1007/978-3-642-21551-3_34

Premium Partner

    Bildnachweise