Economic Capital for the Trading Book

Economic Capital consists of an internally defined amount of capital that is necessary to over- come adverse market conditions. It plays an important role in risk management and business decisions. This thesis focuses on the Economic Capital of the trading book of an international bank Several types of risks need to be modelled and, in this thesis, two risks are investigated, namely market risk and credit risk. For market risk, a model is explained and two risk mea- sures are analysed: Value at Risk and Expected Shortfall. The properties of the estimators of these risk measures are explained and a method to compute the one-year market risk compo- nent based on scaling a risk measure of a 10-day Profit and Loss distribution is derived. This method shows that Expected Shortfall is more appropriate than Value at Risk for modelling tail risk. The second part of this thesis focuses on the migration matrix employed in the model in order to capture the credit risk present in the trading book. Several methods are employed and compared, and a specific method is analysed to assess the probabilities of default in order to be consistent with other probabilities employed by the bank. Furthermore, several characteristics of a rating process are analysed, such as the Markovity and time-(in)homogeneity.Applied mathematicsElectrical Engineering, Mathematics and Computer Scienc