Loss Trigger Leveraged Super Senior Tranche

The loss trigger leveraged super senior tranche (LT-LSS) valuation model is presented. A leveraged super senior tranche trade is a credit linked note, which provides investors with a leveraged exposure to the super senior tranche in a synthetic CDO transaction. The note holder earns the risk premium associated with selling protection on the entire senior exposure when the protection it provides is limited to only the funded principal amount which is just a fraction of the entire exposure.

There are a series of time varying loss triggers built in the trade. If at any time before the trade maturity the accumulated loss amount of the entire collateral pool reaches a predefined level, the trade terminates and is settled on the mark-to-market (MTM) of the underlying super senior tranche or the funded amount, whichever is less.

The valuation of LT-LSS trades has been a challenging task in both the industry and academia. LSS trades are essentially exotic options on the forward starting super senior tranche conditional on the trigger breach, which depends on the way how the correlated default events, credit spread of each reference obligor, and market implied correlations evolve over time. The exercise of a LSS trade is contingent on the trigger breach, which can happen at any time before the trade maturity. The value of the trade cannot be fully determined unless a dynamic process of the portfolio is modeled. Furthermore, compared with other triggers, the LT-LSS is the most complicated because it directly links the credit spread and the implied correlation movements to the default events of the collateral pool. It is almost impossible to get pertinent market information to calibrate such a conditional loss process, even if we can somehow model one.

The model does not attempt to dynamically model the forward starting super senior tranche value conditional on trigger breach. Instead, it makes the assumption that, upon the loss trigger breach, the settlement is always the funded amount which is the maximum payoff of the trade. This assumption enables us to model the LT-LSS trade as a digital trigger option, which can be solved via our recently developed weighted Monte Carlo (WMC) method for the forward starting CDO (FSCDO) trade

For a trade in the sold protection position, the MTM calculated by the LT-LSS model is always conservative. For a trade in the bought protection position, the model is acceptable when an additional model risk reserve is set up.

The LT-LSS model and the FSCDO model share the same model template and the same WMC model. The model risk reserve methodology to address the uncertainties in the WMC method for the FSCDO model applies to the LT-LSS trade. The limitations and restrictions for the LT-LSS model are directly inferred from that of the FSCDO model, except for the choice of calibrating instruments. Compared with the FSCDO model, more spot tranches are needed in the calibration of the LT-LSS model hence it is more difficult to successfully calibrate the model.

A leveraged super senior tranche (LSS) trade is a credit linked note, which provides investors with a leveraged exposure to the super senior tranche in a synthetic CDO transaction. The note holder earns the risk premium associated with selling protection on the entire senior exposure when the protection it provides is limited to only the principal amount that is funded, which is just a fraction of the entire exposure.

• convertible
• convertible pdf