Credit risk is the risk that the counterparty will not settle its liability i.e. the possibility that invested funds will not be recovered in full or within the planned schedule. Credit rating is a forward-looking opinion about credit risk and an assessment of the ability and willingness of an issuer to meet its financial obligations in full and on time. A change in a rating reflects the assessment that the obligor’s credit quality has improved (upgrade) or deteriorated (downgrade). The main goal of this graduate thesis is modeling credit risk of financial institutions by assessing the rating migration probabilities and predicting the probability of default, i.e. of obligor’s failure to meet the legal obligations or conditions of debt repayment, in one or more upcoming periods. Starting from classification of debtor’s riskiness on rating scale, the way from the observed data to the estimated transition probabilities is shown and estimates for the standard deviations of the transition rates are given. Due to interdependencies of borrowers that compose a portfolio, particular emphasis is placed on framework of a threshold normal model with a single parameter which allows us to model dependent rating migrations in consistent way. Regarding time stability of transition matrices, which is one of the major issues for credit risk estimation, next step was to present statistical tests of homogeneity and give proper illustration by an example. Afterwards, multiperiod rating transitions are discussed, relying on Markov chain theory and bootstrap methods for Markov chains. Finally, the change of the composition and riskiness of a credit portfolio caused by rating migrations is considered.