Pricing Multi-Name Default Swaps with Counterparty Risk
by Roy Mashal of Lehman Brothers Inc., and
November 19, 2003
Abstract: We present a simple and general methodology for pricing counterparty risk in multiname default swaps, such as nth-to-default baskets and portfolio loss tranches. The main purpose of our analysis is to derive pricing results without running into the problem of nested valuations, ie, without having to explicitly compute the mark-to-market of the swap in each state where the counterparty defaults. Although the proposed methodology can be used in conjunction with any underlying default model (structural, reduced-form, hybrid), we provide explicit pricing examples for loss tranches of different seniorities by means of a simple and computationally efficient time-to-default simulation, where default dependencies among the reference names and the default-risky counterparty are generated by an appropriately calibrated copula function. We show how fair tranche spreads vary as functions of a) the market-implied default probability of the risky counterparty, b) the asymmetry of the mark-to-market recovery at default, and c) the dependence between the default time of the risky counterparty and the default times of the credits referenced by the swap. Finally, we use our methodology to show that allowing for the possibility of default of the protection seller has a much more significant impact on fair spreads than allowing for the possibility of default of the protection buyer, other things being equal.
Keywords: Counter Party Risk.
Published in: Journal of Fixed Income, Vol. 14, No. 4, (March 2005), pp. 5-16.