Arbitrage-Free Price Ranges for nth-to-Default Swaps

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Arbitrage-Free Price Ranges for n^th-to-Default Swaps

by Michael B. Walker of the University of Toronto

November 29, 2004

Abstract: The arbitrage-free range of values of the loss leg of an nth-to-default swap, and the arbitrage-free range of premium payments for such a swap, are derived for homogeneous baskets of arbitrary numbers of reference entities. Elementary arbitrage arguments are given which show that arbitrage opportunities exist if the prices lie outside of the bounds, and analyses of both a discrete-time model and a continuous-time model show that all prices within the bounds are arbitrage-free.

JEL Classification: C0.

Keywords: n^th-to-default swaps, arbitrage bounds, credit derivatives, basket.