Les approches traditionnelles de calcul du risque tel que la variance, les diff´erentes approches de calcul de la VaR et l’Exepected Shortfall ne s’av`erent pas suffisantes face `a un environnement en perp´etuelle mutation et ils ne tiennent pas compte de
l’attitude de l’investisseur vis `a vis du risque. Dans ce chapitre, on a d´etermin´e, `a par- tir d’un programme de maximisation de l’esp´erance d’utilit´e, une mesure du risque g´en´erale s’appliquant aux fonctions d’utilit´e exponentielle n´egative, iso´elastique ou ” utilit´es CRRA” (constant relative risk aversion) et hyperbolique ou ”utilit´es HARA” (Hyperbolic absolute risk aversion). A titre illustratif, on a appliqu´e ces mesures de risque aux principaux indices boursiers tout en les comparant par les mesures de risque traditionnelles. On a trouv´e que ces mesures sont sensibles au choix des diff´erentes param`etres d’aversion au risque. La variation de cette mesure du risque est une variation positive pour les fonctions d’utilit´e exponentielle n´egative et iso´elastique alors qu’elle change de sens pour la fonction d’utilit´e hyperbolique en fonction des diff´erents param`etres de l’aversion au risque.
Comme nous avons signal´e `a l’introduction g´en´erale, le deuxi`eme objectif de cette th`ese est de d´eterminer une strat´egie de couverture en faisant appel `a l’approche de l’utilit´e esp´er´ee. Une telle strat´egie de couverture s’obtient en minimisant le risque associ´e. Cependant, la litt´erature ´economique sugg`ere qu’il existe une relation entre l’aversion au risque et les densit´es de probabilit´es risque neutre et subjective.
Aat(xT) = p0t(xT) pt(xT) −q 0 t(xT) qt(xT) .
o`u p(.) la densit´e subjective et q(.) la densit´e neutre au risque.
L’estimation la densit´e neutre au risque selon les trois diff´erentes approches pa- ram´etrique, semi-param´etrique et non param´etrique fait l’objet du deuxi`eme cha- pitre. Et l’estimation de l’aversion au risque param`etre fait l’objet du troisi`eme chapitre.
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