CreditRisk+ is one of the most widely implemented credit portfolio models. The independent factor assumption in the original model proposed by Credit Suisse First Boston (1997) underestimates the default correlations among obligors. This thesis introduces three enhanced models that capture the factor covariance structure: Compound Gamma Model, Hidden Gamma Model and Common Factor Model. I compute the portfolio loss distributions generated from these three models via the Fast Fourier Transform (FFT) algorithm. The economic interpretation for the model parameters are also provided. Moreover, the Saddlepoint approximation technique is applied to produce fast and accurate credit Value-at-Risk (VaR) at different levels. The numerical results reveal the ability of the enhanced models to captu...[ Read more ]

CreditRisk+ is one of the most widely implemented credit portfolio models. The independent factor assumption in the original model proposed by Credit Suisse First Boston (1997) underestimates the default correlations among obligors. This thesis introduces three enhanced models that capture the factor covariance structure: Compound Gamma Model, Hidden Gamma Model and Common Factor Model. I compute the portfolio loss distributions generated from these three models via the Fast Fourier Transform (FFT) algorithm. The economic interpretation for the model parameters are also provided. Moreover, the Saddlepoint approximation technique is applied to produce fast and accurate credit Value-at-Risk (VaR) at different levels. The numerical results reveal the ability of the enhanced models to capture the default correlations among obligors. Subsequently, I derive the formulas for VaR contributions in the three enhanced CreditRisk+ and perform numerical tests to show their stability. As one of the applications of the CreditRisk+, I estimate the expected tranche losses of CDO with the Compound Gamma Model and Hidden Gamma Model. Based on the modeling analysis and numerical studies, the enhanced CreditRisk+ models are appropriate choices to model default correlation with respect to different financial situations.