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Exact Replication of k-th-to-Default Swaps with First-to-Default Swaps

by Hans-Juergen Brasch of Rabobank International

February 20, 2006

Abstract: This article establishes some basic relationships between k-th-to-default events in a credit basket and first-to-default events in sub-baskets. We exploit the observed properties to determine relationships between the corresponding probability distributions. One possible application is the pricing and replication of a k-th-to-default swap with first-to-default swaps on sub-baskets. This replication can be adapted to synthetic tranche pricing, in particular, for the trading of tranche-lets in the equity tranche bracket. Moreover, the additional insight into the basket probability distribution provides a useful tool to test basket models for consistency. In particular, when some model aspects are based upon parameter mappings or interpolation routines.

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