Many achievements in the modelling of risk, which are connected with the development of financial mathematics are primarily related to market risk rather than credit risk. Nevertheless, recent years have seen a growing interest arising in credit risk, mainly caused by the increasing competition in the banking sector, the blooming secondary credit market based on securitisation, as well as the development of credit derivatives.

Models describing the risk of a single loan (so-called scoring methods) are considerably more developed and more often applied than the models which concern the risk of the whole credit portfolio. Despite the fact that, in most cases, a profit or a loss generated by a bank depends on a skilful risk management of a whole credit portfolio, the development of methods supporting these decisions is obstructed by a number of factors. Key problems include low availability of data that inhibits scientific research and difficulties in applying the classical theory of Markowitz' portfolio analysis in practice and they arise primarily from the very low liquidity of the loans and the absence of some unambiguous methods to measure return on loans and the risks of individual credit contracts. However, it was the classical theory formulated by Markowitz which underlay the development of the first models describing behaviour of credit portfolio risk by Gollinger, Morgan and Altman. However, for the reasons stated above, these models could not serve as the basis for the development of commonly used commercial products. Their fate was also shared by the models prepared by Bennet, Chirinko and Guilla, in which they tried to show the connections between the macroeconomic processes and the quality of credit portfolio. Only the most recent models such as CreditPortfolioView, Credit Metrics or CreditRisk+ have fully complied with the demands of the market. Their success can be attributed to the fact that they have been developed by commercial companies for commercial purposes. However, the origins of these approaches vary. The first above-described model is an econometric model, which uses Monte Carlo methods; the second one is based on the use of the enterprise behaviour model proposed by Merton, while the third relates directly to actuarial mathematical techniques. They use Value at Risk as the base measurement of the credit portfolio risk and refer to Monte Carlo methods to a larger or smaller extent. The article offers a detailed analysis of all the above-mentioned approaches, both theoretical ones as well as those that have been adopted in practice.