Small perturbations with large effects on value-at-risk
Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) no. 1-2.

Voir la notice de l'article dans Library of Science

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.
Mots-clés : Gaussian perturbation, value-at-risk, delta-normal model 
@article{DMPS_2013_33_1-2_a9,
     author = {Esqu{\'\i}vel, Manuel and Dimas, Lu{\'\i}s and Mexia, Jo\~ao and Didier, Philippe},
     title = {Small perturbations with large effects on value-at-risk},
     journal = {Discussiones Mathematicae Probability and Statistics},
     publisher = {mathdoc},
     volume = {33},
     number = {1-2},
     year = {2013},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a9/}
}
TY  - JOUR
AU  - Esquível, Manuel
AU  - Dimas, Luís
AU  - Mexia, João
AU  - Didier, Philippe
TI  - Small perturbations with large effects on value-at-risk
JO  - Discussiones Mathematicae Probability and Statistics
PY  - 2013
VL  - 33
IS  - 1-2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a9/
LA  - en
ID  - DMPS_2013_33_1-2_a9
ER  - 
%0 Journal Article
%A Esquível, Manuel
%A Dimas, Luís
%A Mexia, João
%A Didier, Philippe
%T Small perturbations with large effects on value-at-risk
%J Discussiones Mathematicae Probability and Statistics
%D 2013
%V 33
%N 1-2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a9/
%G en
%F DMPS_2013_33_1-2_a9
Esquível, Manuel; Dimas, Luís; Mexia, João; Didier, Philippe. Small perturbations with large effects on value-at-risk. Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) no. 1-2. https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a9/

C. Alexander, Value-at-Risk Models (John Wiley Sons, 2008).

P. Best, Implementing Value at Risk (John Wiley Sons, 1998).

M. Choudry, An Introduction to Value-at-Risk, fourth edition (John Wiley Sons, 2006).

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).

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

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

P. Embrechts and A. Hing, Extreme VaR scenarios in higher dimensions, Extremes 9 (3) (2006) 177-192. doi: 10.1007/s10687-006-0027-6

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

W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II (John Wiley Sons, 1971).

P. Jorion, Value at Risk, third edition, McGraw-Hill (New York, 2007).

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

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

A. McNeil, and R. Frey and P. Embrechts, Quantitative Risk Management (Princeton University Press, 2005).

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

W.R. Pestman, Mathematical statistics (Walter de Gruyter Co, Berlin, 1998). doi: 10.1515/9783110208535

R. Rebonato and P. Jäckel, The most general methodology to create a valid correlation matrix for risk management and option pricing purposes, preprint.

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.

A.N. Shiryaev, Probability (Springer-Verlag, 1996). doi: 10.1007/978-1-4757-2539-1