Modelling of risk is of paramount importance for financial institutions, as they have strong incentive to be protected against default events and are required to comply with numerous regulations. For better understanding we introduce a global overview across market, operational and credit risk with putting a focus on former one. This paper makes an attempt to investigate probability of default in retail banking sector using several mathematical approaches: statistical models, probabilistic models, bayesian statistics, machine learning and classification analysis. More specifically, we selected models from various different domains which are tailored to best model real world data: Merton model, Linear and Quadratic Discriminant Analysis, Support Vector Machines (SVMs) and Markov Chains. We will conclude with an empirical analysis to test each model under certain initial assumptions and conduct a thorough evaluation, discussing advantages and disadvantages of each model and suggesting potential improvements.