Optimization of Collateral Allocation for Corporate Loans : A nonlinear network problem minimizing the expected loss in case of default

Sammanfattning: Collateral management has become an increasingly valuable aspect of credit risk. Managing collaterals and constructing accurate models for decision making can give any lender a competitive advantage and decrease overall risks. This thesis explores how to allocate securities on a set of loans such that the total expected loss is minimized in case of default. A nonlinear optimization problem is formulated and several factors that affect the expected loss are considered. In order to incorporate regulations on collateral allocation, the model is formulated as a network problem. Finally, to account for the risk of the portfolio of securities, the Markowitz approach to variance is adopted. The model calculates a loss that is less than the average historical loss for the same type of portfolio. In the case of the network problem with many-to-many relations, an equal or higher expected loss is concluded. Similarly, when the variance constraint is included, the expected loss increases. This is due to some solutions are limited when removing links and including the variance constraint. The optimization problem is forced to choose a less optimal solution. The model created has no limits on the amount of collateral types and loans that can be included. An improvement of the model is to account for the stochasticity of the collateral values and the difficulties in validating the results. The latter is a consequence of the expected loss functions being based on a theoretical analysis. Nonetheless, the results of the model can act as an upper bound on expected loss, with a certain variance, since the average of the expected loss lies above the average of the historical loss.