A tree-based approach to price leverage super-senior tranches

The recent liquidity crisis on the credit derivative market has raised the need for consistent mark-to-model valuation method for some exotic products such as leverage super-senior tranches. Roughly speaking, a Leverage Super-Senior (LSS) tranche is a path-dependent option on the market-value of a traditional super-senior tranche. This option is exercised at the first moment when a particular threshold is hit by a pre-specified trigger proxy. There are three types of proxies commonly used in LSS structures: the pool default losses, the weighted average of CDS spreads and the market-value of the super-senior tranche. We show that the model proposed in Laurent et al. (2007) can be easily adapted to assess the risk of LSS structures and their fair value. In the latter paper, the dynamics of the loss process can be described through a recombining binomial tree and transition probabilities can be calibrated on liquid tranche quotes. In this note, we detail the computation of LSS present values along the nodes of the tree, given that standard option triggers – loss-only trigger, spread trigger or market value trigger – are all stopping times with respect the the loss filtration.