Journées de l'optimisation 2007 Optimizations days

Ce modèle est largement utilisé dans les banques centrales et autres institutions financières afin d'estimer la structure à terme des taux d'intérêt. La calibration de ce modèle exige, à chaque moment où une courbe est requise, la minimisation de la distance entre les prix des obligations théoriques et observés. La fonction à quatre paramètres à optimiser possède plusieurs optimums. Nous présentons une procédure d'optimisation qui réduit la dimension du problème de sorte qu'une recherche par treillis peut efficacement être mis en place afin de limiter la probabilité de rester captif d'un optimum local. Nous présentons aussi une procédure randomisée permettant d'estimer la probabilité d'avoir atteint l'optimum global.

Recent empirical evidence highlights the importance of asymmetries in the extremes of the dependence structure of asset returns. In this paper I propose a model that is able to address this feature of the data based on the construction of a multivariate diffusion with pre-specified stationary distribution using copula functions and study its effect on portfolio choice in a complete market setup where optimal allocation rules are obtained analytically under the Martingale technique using Malliavin calculus.

This paper presents a reduced form model for the valuation of variable-coupon bonds where the coupon rate fluctuates with the credit rating of the issuing firm. We work within a class of intensity based pricing models where a Cox (or a doubly stochastic Poisson) process governs the intensity of the ratings change. The time-variation in the credit transition process is modeled via a continuous-time inhomogeneous Markov chain. With a desire to avoid making strong assumptions on the properties of the generator matrix, we develop a general recursive pricing model. As a special case, we derive essentially closed form solutions for the prices of step-up only bonds within an affine term structure setting.

Based on the methodology of Jafry and Schuermann (2004) to summarize the rating transition matrix into a scalar, we build up time series of these indices for each US business sector. The database used consists on rating transitions reported by Moody's from the first quarter of 1980 to the first quarter of 2005. As a first step, we check if the mobility index used captures some stylized facts. For instance, we confirm the existence of rating momentum effects for the majority of US business sectors. Then, we test for possibly crisis transmission phenomenon among sectors by estimating a Markov Switching Vector Autoregressions model. The results obtained provide evidence of high and low correlation regimes and prove default contagion among some sectors.