Valuation and optimization of credit risk using a portfolio model

In this paper I study a model for credit risk in a portfolio of sovereign bonds, based on (van der Hoorn, 2009). The model is based on historical credit rating changes and the joint distribution of the losses for di erent bonds is modeled with an assumption of an underlying multivariate Gaussian variable. Di erent risk measures for the portfolio are calculated using Monte Carlo simulations and the performance is improved by the use of importance sampling. I investigate di erent methods on how to improve the model and the estimation of the parameters of the model. I also develop methods to valuate the certainty of the risk measures based on a statistical view on the input data, which give clear indications that the small size of input data gives low accuracy for the risk measures. An attempt to write an algorithm to nd the optimal portfolio with respect to the risk measures is also performed and the results are discussed.