After being provided with motivation for development of quantitative methods of studying risks in the first chapter, the following chapter is devoted to studying one of many possible approaches to risk modelling. We then introduce basic concepts using the examples of stock-portfolio modelling and portfolio credit risk. Finally, two outspreaded risk measures are explained, namely VaR and ES (expected shortfall). Taking the example of loss modelling using two different distributions (normal and Student t-distribution), we note some benefits of using expected shortfall, instead of VaR, as a risk measure. Third chapter is dedicated to three well-known credit risk models. First model, developed by Robert C. Merton, is among the most famous ones due to its influence on the evolution of the theory and its implementation in financial industry. As an example of an industrial model, KMV model is explained more thoroughly. Although it is somewhat an extension of the Merton model, KMV model uses data from big databases of companies which have previously defaulted in similar conditions when estimating a specific probability of default. Third model we examine uses credit ratings obtained from independent agencies in analyzing future credit solvency. Last section of the thesis is devoted to analyzing another approach to modelling a credit risk portfolio- the one based on previously addressed structural models. We are particularly interested in both correlation of defaults of two different counterparties, and the probability of simultaneous defaults of more counterparties. Here the key role is played by joint distribution function of critical variables, whose fall below some preset level symbolizes a default. By introducing copulas, different possibilities of joint distribution function selection are considered. Finally, taking the last exhibited example into consideration, it is possible to acknowledge the importance of choosing as precise joint distribution function as possible, since a less adequate selection can lead to underestimating the weight of the right tail of portfolio loss distribution.