Theoretical and Computational Analysis of Credit and Liquidity Risk with Multiple Defaults

Since the 2008 global financial crisis, regulators have been paying considerable attention to the credit and liquidity risks. Two such concepts (related to credit and liquidity risks) that have been repeatedly mentioned in the regulatory announcements are the credit value adjustment (CVA) and the Incremental Risk Charge (IRC).

The CVA is an adjustment to the previous trade price when the counterparty risk has been added. The IRC is a new type of risk charge defined in Basel II which covers the major exposures of the counterparty and liquidity risk in the trading book.

The current models on CVA and IRC have specific shortcomings. The CVA is currently calculated on a one-period model with restriction on the number of defaults. The IRC is computed using the time consuming Monte Carlo simulations.

In this dissertation, we have made significant contributions to risk analysis by solving CVA in both two-default and full model without the restriction on the number of defaults as well as providing an analytical method for calculating IRC. Our research can be considered as a major step forward in expanding the current credit and liquidity risks models.

Compared to the current one-default CVA calculations, our two-default and full calculations offer the distinct advantages of more accurate and practical CVA results. On top of that, our PDE method provides the speed and accuracy which allows us to finish a thorough risk exposure analysis and identify the conditions when the first default CVA overestimates or underestimates the counterparty risk.

As opposed to the current numerical approach of calculating IRC, we offer an analytical method which provides an approximation of VaR on the two-period model and exact value of VaR on the infinite-default model. This is the first analytic solution in the literature on the multi-period capital model and may impact the view of current measure of risk controls in the banks. Thus credit risk control can be greatly improved if this new analytic solution can be applied in financial industry.

Combined together, the work in this dissertation makes significant improvements in credit risk analysis in the multi-period credit and liquidity risks models.