Optimization of cash flows associated with synthetic CDOs.
Collateralized Debt Obligations are exotic derivatives used to perform securitization. CDOs are not as widely used nowadays as they were before the Subprime crisis of 2007. Nonetheless it remains an enthralling challenge to optimize cash flows associated with synthetic CDOs. In our paper, we only deal with synthetic CDOs. This derivative is only composed of Credit Default Swaps and layered in different tranches. The tranche chosen by the investor sets the number of CDSs affected by the operation of buying or selling. The investment is all the more risky as the number of CDS is low. However, the prime leg will be higher.
We use a Binomial based model (considered Gaussian due to the size of our population which is equal to 125) in which default correlation and unconditional probability of default are highlighted. Thousands of simulations are then performed based on this model and in different scenarios in order to evaluate the associated cash flows given a specific number of defaults at different periods of time. Cash flows are not solely calculated on a single bought or sold tranche but rather on a combination of bought and sold tranches. Thanks to logical filtering we deduce strategies regarding a given synthetic CDO and evaluate the P&L according to each of them. Then the results obtained are visualized in order to highlight the most relevant strategies and reveal the synthetic CDO’s potential through the Principal Component Analysis.
Furthermore, our wish to implement a method to optimize the several hundred strategies we obtained lead us to put in place the Simplex method. The pre-requisite consisted of the two aforementioned parameters, unconditional probability of default and default correlation. The first one, using the Bootstrap method on Matlab, is set and the second one varies on its domain of definition (0-0.3). Hence, for each default correlation value, we can calculate the default occurrence and determine each tranche-associated cash flow. The Simplex method is useful to ascertain the best combination of bought and sold tranches for each deadline. The establishment of a pattern outputs a surface depending on maturity and default correlation. The best combination of maturity and default correlation can be found on the steepest slope’s radius of curvature.
The Gaussian model we use is not so to say realistic in crisis situations. Besides we have not made our system able to handle buying or selling a portion of a tranche but only the whole tranche. However our work gives relevant means to the investor on how he can proceed to know what to buy and sell.