HedgingMG2

Le modèle G2++ (modèle gaussien à deux facteurs) est un modèle de taux introduit en 2005 par Brigo et Mercurio.

Le modélisation de la courbe des taux se fait via deux facteurs stochastiques (l’un modélisant le niveau de la courbe et l’autre sa pente) et un troisième facteur déterministe. On peut pricer différents produits dérivés de taux (caps, floors, swaptions, options sur obligations, FRA …) grâce à des formules explicites tirées de ce modèle.

Notre projet de fin d’étude a donc porté sur la réalisation d’un logiciel portant sur l’utilisation pratique de ce modèle de taux qu’est le modèle Gaussien à deux facteurs. Le logiciel permet à l’utilisateur (gestionnaire de portefeuille) de couvrir un portefeuille d’obligation sur une possible variation des taux d’intérêts tel qu’il l’envisage. Implémenté en VBA, il est facile d’utilisation, intuitif et performant. En effet, l’utilisateur est guidé dès l’ouverture du logiciel.

La page “Accueil” lui explique la procédure à suivre pour bien utiliser le logiciel. La seconde feuille (“Données utilisateur”) lui permet de saisir ses propres informations de marché : d’une part pour calibrer le modèle et d’autre part pour qu’il saisisse sa prévision de variation des taux d’intérêts. Sur la feuille “Portefeuille t”, l’utilisateur entre les différentes informations de ses obligations.

De ces données sont calculées la duration, la sensibilité et la convexité pour enfin trouver la DV01 de chacune des obligations. Une fois la saisie terminée et la couverture lancée, le logiciel va calculer les taux forwards suivant les paramètres du modèle G2++ (a : vitesse de retour à la moyenne du premier processus stochastique du modèle, b vitesse de retour à la moyenne du second processus stochastique, sigma : volatilité du premier processus, eta : volatilité du second processus, rho : corrélation entre les deux processus) entrés par l’utilisateur.

A partir de ces taux forwards, le logiciel price les produits dérivés à l’aide du modèle. Après déplacement des taux d’intérêts, un nouveau calcul des taux forwards est effectué pour enfin pricer à nouveau les produits dérivés. De ces calculs est tirée la DV01 de chacun des dérivés de taux et le logiciel hedge le portefeuille afin de trouver la couverture la plus adéquate pour le scénario de l’utilisateur. Les résultats sont affichés sur la feuille “Portefeuille t+1”.

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