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Throughout the global financial crisis that arose in 2007–2008, very large companies and even sovereign states defaulted or were on the point of defaulting. This situation raised the vigilance of risk managers about their risk assessment. The general image about Credit Risk Agencies (CRA) has also been shaken and weakened by the crisis.

A great tool to quantify the counterparty credit risk is the probability of default (PD), which has also an effect on pricing of derivatives and loans. Since a few years, the Markov chain method became a norm to estimate PD and even migration matrices.

In this paper, a focus is made on long-term foreign currency credit ratings for sovereign bonds and more precisely, on the subsample containing advanced companies. An approach to implementing the Markov chain method in both discrete and continuous time is addressed. An implementation of this method and the literature about the subject permitted to conclude that the continuous time is more advantageous.

Furthermore, a study of the time-homogeneity assumption is taken and showed that this assumption is a simplification and is usually wrong. The evolution of both the advanced economies and the other sovereign states through the economic cycle is also investigated. By using recession and expansion migration matrices, large differences of estimated PDs over the economic cycle were found. Also the investigation of advanced economies allowed to state that advanced companies are much less submitted to credit rating downgrades than other sovereign states.

Matrice de transition --- Probabilité de défaut --- Chaîne de Markov --- Agence de notation --- Notation financière --- Sciences économiques & de gestion > Finance

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Biomathematics. Biometry. Biostatistics --- Statistical physics --- Stochastic processes --- Modèle mathématique --- Mathematical models --- Méthode statistique --- Statistical methods --- Wiskundige natuurkunde --- Biomathematica. --- Stochastiques (Processus) --- Physique mathématique --- Biomathématiques. --- Stochastische processen. --- Analyse mathematique --- Probabilite --- Interacting systems --- Ising models --- Spin systems --- Markov processes --- Markov chain --- Nearest-neighbour --- Chaine de markov --- Nearest particle system --- Exclusion process

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Ecology --- Mathematical models --- Simulation methods --- Écosystème --- ecosystems --- Modèle --- Models --- methods --- Évaluation --- evaluation --- Biotic communities --- Computer simulation --- evaluation. --- Ecology - Mathematical models --- Ecology - Simulation methods --- Chaine de markov --- Equation de chapman-kolmogorov --- Matrice de leslie et husher --- Model sylver spring --- Simulation monte carlo

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Ce mémoire retrace l'histoire de quelques points des probabilités jusqu’à l’axiomatique de Kolmogorov. Dans un premier temps, nous nous intéressons au problème initial qui a suscité l’intérêt de calcul des probabilités et son développement menant aux différentes approches de la probabilité. Dans un second temps, nous analysons dans quelques manuels scolaires les plus utilisés par les enseignants de mathématique en Fédération Wallonie Bruxelles la place de ces différentes approches de la probabilité et nous apporterons quelques remarques nécessaires.

Problèmes des partis --- distribution des mises --- la valeur du sort --- espérance conditionnelle --- équation de récurrence d'ordre 2 --- ruine de joueur --- approche cardinaliste --- approche fréquentiste --- approche axiomatique --- processus stochastique --- chaîne de Markov --- analyse de manuels scolaires --- Physique, chimie, mathématiques & sciences de la terre > Mathématiques