This thesis studies the problem of computing adjustments for bilateral
counterparty risk for a standard Credit Default Swap (CDS) in a three-factor first passage time default risk model.

Extending the existing literature that gives analytical expression for the transition probability density function for two-dimensional Brownian motions absorbed at the boundaries in the positive quadrant, a method to obtain a semi-analytical expression for the transition probability density function of a three-dimensional Brownian motion absorbed at first exit time from the positive octant is developed. This is done by separating the problem into a radial and an angular part, of which the latter depends only on the correlation matrix. The solution to the angular part is obtained through the finite element method.

These mathematical results are then used to provide semi-analytical expressions for bilateral Credit Value Adjustment (CVA) and Debit Value Adjustments (DVA) of a credit default swap. An example of market data is analysed in detail and it is shown that these value adjustments can be non-negligible. An approximation commonly used by practitioners for the computation of bilateral value adjustments is to use the sum of the unilateral ones as a proxy. The framework developed here allows for an analysis on the precision of this approximation to be performed in the case of the credit default swap, when wrong-way risk is present. Finally, the problem of valuing partially collateralised CDSs is studied and analytical or semi-analytical solutions are developed for computing the potential shortfall caused by the risky nature of the collateral.