Measuring credit risk of a loan portfolio: a comparison of different probability of default models

A portfolio consisting of loans is extremely sensitive to credit risk, thus many products have been developed over time trying to insure this credit risk. Different models trying to capture credit risk within the portfolio have been developed, often consisting of a probability of default part and a recovery rate part. This paper looks at three main forms of modelling the probability of default, a form of historical simulation, the advanced IRB model and the CreditRisk+ model. I look at the strengths and weaknesses of these models and show the three approaches all converge to a similar outcome when looking at a portfolio spread across different ratings and covers a longer period of time. Solutions to some of the weaknesses are looked at, such as using historical probability of default data to include past knowledge within the advanced IRB model. Lastly a mixed model will be looked at, which is a combination of historical simulations and the advanced IRB model. The different models are validated within this paper, showing all three approaches to be valid options and showing these models can be used by companies depending on other reasons such as using the model specifically for sector loans.