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Home > Resources > WIKI

What is a Basket Default Swap

A basket default swap is similar to a single entity default swap except that the underlying is a basket of entities rather than one single entity. There are several types of basket default swaps. The popular ones are first-to-default, n-th-to-default, n-out-of-m-to-default and all-to-default swaps. With a single entity, a credit event is usually a default of the entity. With a first-to-default swap, a credit event occurs the first time any of the entities defaults. Such a swap will provide default protection against losses related to this first default. A similar definition holds for an n-th-to-default swap. An n-out-of-m-to-default swap protects the buyer against losses related to the first defaults of the m-entity basket. Similarly, an all-to-default swap protects against losses resulting from credit events of any of the entities in the basket.

For a first-to-default default swap, whenever an entity in the reference basket defaults, the buyer stops paying the swap's premium and receives from the seller the difference of the principal amount of the defaulted entity and the recovered value. If the swap's counterparty defaults, premium payments will stop and both the buyer and the seller walk away from the contract. For an n-th-to-default swap whenever the n-th default occurs in the reference basket, the buyer stops paying the premium and receives the difference of the principal amount of the latest (n-th) defaulted entity and the recovered value. Note that the premium does not stop until the n-th default as long as the counterparty does not default, even if there are already defaults in the basket. For an n-out-of-m-to-default swap the seller pays the difference of the principal amount and the recovered value for each of the first defaults and the buyer stops paying the premium after the n-th default occurs. For an all-to-default swap the buyer continues paying the premium as long as there are undefaulted entities in the basket and the counterparty does not default, and receives from the seller any lost principal amount of the basket.

FINCAD provides functions for valuing basket default swaps with correlated or independent defaults. These functions can also handle counterparty default risk. One basic assumption is that no two entities can default at exactly the same time. This is equivalent to saying that the credit index correlation matrix of the reference entities must be positive definite, or in other words, perfect correlation is not allowed.

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