Static Replication

Abstract

In principle, the direct (pricing) method requires, for each time step, $2^{n+1}$ values, corresponding to the set of all possible default combinations; as the size of the underlying basket increases, the number of default configurations explodes exponentially. This significant limitation restricts the applicability of the method to baskets under 10 or 11 credits. As an alternative, we develop a different approach, which is based on a static replication idea. In this chapter, we describe how this static FTD replication is done: first, we show the relationship between kth-to-default and $(k-1)$th-to-default swaps; then, we apply this recursion step-by-step until we arrive at the complete FTD expansion.