During the last decades, credit risk has been proved one of the greatest risks an institution is facing. This fact has forced banks and regulators all over the world to reassess the importance of credit risk and establish it as a core concept on their everyday activities. This thesis presents credit risk measurement approaches, using transition probability matrices, which have a substantial effect on loan pricing. Through recent years a method using Markov chains, in order to calculate transition probabilities and probability of default has evolved and has been established as an industry standard for both continuous and discrete time periods. Moreover this thesis investigates the different assumptions, that are crucial for our model implementation and statistical measures that help us to investigating whether these assumptions hold true. Finally we will present other measures related to transition probability matrices which are, crucial for decision making in the banking sector.