Credit risk is one of the most important types of risk that any financial institution must face with. In the financial world, the essence of control relies on how well the model mimes reality and on the precision of the computational methods used. In this thesis, we consider the most common credit risk models: “CreditRisk+” of Credit Suisse Financial Product, and the Gaussian and t-copula models. All of them belong to the Bernoulli mixture models, used in literature for tractability reasons, and for their generical modeling approach. We, therefore, focus on Bernoulli mixture models, without loss of generality. We consider the case of homogeneous portfolios, i.e.