Reference : Modélisation d'évènements rares à l'aide de distributions non normales : application ...
Dissertations and theses : Master's dissertation
Business & economic sciences : Quantitative methods in economics & management
Modélisation d'évènements rares à l'aide de distributions non normales : application en finance avec la fonction sinh-arcsinh
[en] Modeling of rare events using non-normal distributions : an application in finance with the sinh-asinh distribution
Hambuckers, julien mailto [Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie >]
Université de Liège, ​​Belgique
Master en Ingénieur de gestion, à finalité spécialisée en Finance et Contrôle
Heuchenne, Cédric mailto
Van Caillie, Didier mailto
Haesbroeck, Gentiane mailto
[en] sinh-asinh ; leptokurtic ; GARCH ; Value-at-Risk ; VaR ; non-parametric ; market risk
[en] In 2008, the financial crisis put forward the relative inaccuracy of the market risk forecasting
models in the financial industry. In particular, extreme events were shown to be regularly
underestimated. This problematic, initially developed in the seminal work of Mandelbrot
(1963), is mainly due to financial models using the normal law while empirical evidence show
strong leptokurticity in financial time series. This stylized effect is particularly damaging the forecasting of indicators like Value-at-Risk (VAR). In this study, we try to tackle problem by testing a newly-developed probability distribution, never used in finance: sinh-arcsinh function. By creating different datasets from non-parametric and GARCH
models, we adjust common functions (normal, t location-scale, GED, gen. hyperbolic) and sinh-arcsinh function on the data. We show that, regarding the leptokurtic datasets extracted
from the DJA and the NIKKEI 225, the sinh-arcsinh function performs a better adjustment
than any other function tested. We also tested simple VAR models using normal laws,
Student’s t or sinh-arcsinh functions, to assess the operational efficiency of the sinh-arcsinh
function. We show that models using sinh-arcsinh functions provide more accurate and better
in-sample and out-of-sample VAR forecasts than any other model using the normal laws.

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