First-loss and Tranche-loss Credit Default Swaps
Similar to a first-to-default or an nth-to-default credit default swap, a first-loss credit default swap (FLCDS) protects its buyer from losses of a reference asset pool as a result of credit events. The buyer of an FLCDS is compensated when a reference asset incurs a credit event. In return the buyer pays premiums periodically, in a lump sum, or in both forms, until a termination condition has been met.
Unlike a first-to-default credit default swap, in which only the loss from the first credit event is compensated, or an nth-to-default credit default swap, in which the losses from the nth default or the first n defaults are compensated, an FLCDS compensates its buyer for any losses from credit events of the reference assets up to a certain portion of the total notional of the asset pool. In the former, the maximum number of defaults is defined and known beforehand but the maximum loss amount is, in general, unclear, while in the latter the maximum loss amount is clearly defined and known beforehand but the maximum number of credit events is, in general, unknown. Another important difference is that, in the former, the premium leg notional remains constant until the contract terminates, while in the latter the premium notional varies, and amortizes when a loss of the pool occurs or when an asset matures.
A more general form of a first-loss credit default swap is a basket-linked credit default swap, where the buyer is protected from a range of cumulative losses of a reference pool. For example, a 5-10% credit default swap compensates a buyer from any losses that exceeds 5% of the initial total notional of the pool, and the maximum compensation is:
(1)
where
is the initial notional of the pool.
Such a generalized first-loss credit default swap is referred to as a tranche-loss (or a layer-loss) credit default swap (STCDS) in this document and other FINCAD products.
An important class of first loss or tranche loss credit default swaps is the so-called standardized tranche credit default swaps. Here the reference asset pool is a collection of credits, typically names of investment grade companies, and each credit has the same amount of notional and the same recovery rate. To meet the needs of investors with different appetites for risk, the loss severity of the credit pool is divided into several levels, called tranches. Each tranche has a notional. If a credit event occurs in the reference credit pool, the lost notional minus the recovered amount will be subtracted from the tranches. The tranche with the lowest rank takes the first loss of the pool. Other tranches can tolerate certain degrees of loss and will suffer loss when all its subordinate tranches have suffered full losses. The level of subordination of a tranche is often called an attachment point. The maximum loss, as a portion of the total pool notional that will result in the full loss of the notional of a tranche, is called a detachment point. The detachment point of a tranche is the attachment point of the tranche with the next higher ranking. For an example, a tranche with an attachment point of 4% and a detachment point of 10% will not suffer any loss if the accumulated loss of the pool is no more than 4%, and any loss that is more than 4% will eat into this tranche until all of its notional is gone. Since the notional and the recovery of each credit in the tranche are the same, similar to the nth-to-default swap, the attachment and detachment points can be expressed in numbers of defaults, although these numbers can be decimal.
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