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2013 | 33 | 1-2 | 151-169
Tytuł artykułu

Small perturbations with large effects on value-at-risk

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.
Rocznik
Tom
33
Numer
1-2
Strony
151-169
Opis fizyczny
Daty
wydano
2013
otrzymano
2013-08-14
poprawiono
2013-11-15
Twórcy
  • Departamento de Matemática FCT/UNL e CMA/FCT/UNL, Quinta da Torre, 2829-516 Caparica, Portugal
autor
  • Colégio Militar Largo da Luz, 1600-498 Lisboa, Portugal
  • Centro de Matemática e Aplicações da Universidade Nova de Lisboa (CMA/FCT/UNL), Quinta da Torre, 2829-516 Caparica, Portugal
  • Departamento de Matemática FCT/UNL e CMA/FCT/UNL, Quinta da Torre, 2829-516 Caparica, Portugal
Bibliografia
  • [1] C. Alexander, Value-at-Risk Models (John Wiley & Sons, 2008).
  • [2] P. Best, Implementing Value at Risk (John Wiley & Sons, 1998).
  • [3] M. Choudry, An Introduction to Value-at-Risk, fourth edition (John Wiley & Sons, 2006).
  • [4] L. Dimas, Sobre a Influência de Pequenas Perturbações no Cálculo do 'Value-at-Risk' de uma Carteira de Activos, Master of Science Dissertation, Text in Portuguese (Universidade Nova de Lisboa, 2014).
  • [5] P. Embrechts, J. Nešlehová and M. Wüthrich, Additivity properties for value-at-risk under Archimedean dependence and heavy-tailedness, Insurance Math. Econom. 44 (2) (2099) 164-169. doi: 10.1016/j.insmatheco.2005.01.006
  • [6] P. Embrechts, A. Höing and G. Puccetti, Worst VaR scenarios, Insurance Math. Econom. 37 (1) (2005) 115-134. doi: 10.1016/j.insmatheco.2005.01.006
  • [7] P. Embrechts and A. Hing, Extreme VaR scenarios in higher dimensions, Extremes 9 (3) (2006) 177-192. doi: 10.1007/s10687-006-0027-6
  • [8] C.G. Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math. 77 (1945) 1-125. doi: 10.1007/BF02392223
  • [9] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II (John Wiley & Sons, 1971).
  • [10] P. Jorion, Value at Risk, third edition, McGraw-Hill (New York, 2007).
  • [11] R. Kaas, Roger J.A. Laeven and Roger B. Nelsen, Worst VaR scenarios with given marginals and measures of association, Insurance Math. Econom. 44 (2) (2009) 146-158. doi: 10.1016/j.insmatheco.2008.12.004
  • [12] Roger J.A. Laeven, Worst VaR scenarios: A remark, Insurance Math. Econom. 44 (2) (2009) 159-163. doi: 10.1016/j.insmatheco.2008.10.006
  • [13] A. McNeil, and R. Frey and P. Embrechts, Quantitative Risk Management (Princeton University Press, 2005).
  • [14] M. Mesfioui and J.F. Quessy, Bounds on the value-at-risk for the sum of possibly dependent risks, Insurance Math. Econom. 37 (1) (2005) 135-151. doi: 10.1016/j.insmatheco.2005.03.002
  • [15] W.R. Pestman, Mathematical statistics (Walter de Gruyter & Co, Berlin, 1998). doi: 10.1515/9783110208535
  • [16] R. Rebonato and P. Jäckel, The most general methodology to create a valid correlation matrix for risk management and option pricing purposes, preprint.
  • [17] K. Schöttle and R. Werner, Improving the most general methodology to create a valid correlation matrix, in: Risk Analysis IV, Wessex Institute of Technology Press.
  • [18] A.N. Shiryaev, Probability (Springer-Verlag, 1996). doi: 10.1007/978-1-4757-2539-1
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1148
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