Optimal Structuring of CDO contracts: Optimization Approach

The objective of this paper is to help a bank originator of a Collateralized Debt Obligation (CDO) to build a maximally profitable CDO. We consider an optimization framework for structuring CDOs. The objective is to select attachment/detachment points and underlying instruments in the CDO pool. In addition to ”standard” CDOs we study so called ”step-up” CDOs. In a standard CDO contract the attachment/detachment points are constant over the life of CDO. In a step-up CDO the attachment/detachment points may change over time. We show that step-up CDOs can save about 25%-35% of tranche spread payments (i.e., profitability of CDOs can be boosted about 25%-35%). Several optimization models are developed from the bank originator prospective. We considered a synthetic CDO where the goal is to minimize payments for the credit risk protection (premium leg), while maintaining a specific credit rating (assuring the credit spread) of each tranche and maintaining the total incoming CDS spread payments. The case study is based on the time to default scenarios for obligors (instruments) generated by Standard & Poor’s CDO Evaluator. The Portfolio Safeguard package by AORDA.com was used to optimize performance of several CDOs based on example data. Introduction The market of credit risk derivatives was booming before the recent financial crisis. Collateralized Debt Obligations (CDOs) accounted for a significant fraction of this market. The appeal of CDOs was in their high profit margins. CDOs offered returns that were sometimes 2-3% higher than corporate bonds with the same credit rating. The recession seems to be over now and banks keep searching for new opportunities with credit risk derivatives. Optimal structuring techniques may help to increase the profitability of CDOs and other similar derivatives. A CDO is based on so called “credit tranching”, where the losses of the portfolio of bonds, loans or other securities are repackaged. The paper considers synthetic CDOs in which the underlying credit exposures are taken with Credit Default Swaps (CDSs) rather than with physical assets. The CDO is split into different risk classes or tranches. For instance, a CDO may have four tranches (senior, mezzanine, subordinate, and equity). Losses are applied to the later classes of debt before earlier ones. From the underlying pool of instruments, a range of products are created ranging from a very risky equity debt to a relatively riskless senior debt. Each tranche is specified by its attachment and ∗Risk Management and Financial Engineering Lab, Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL 32611, E-mail: {averemyev, tsyurmasto, uryasev}@ufl.edu †Current address: Munitions Directorate, Air Force Research Laboratory, Eglin AFB, FL 32542 ‡Corresponding author