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Hedging Portfolio Loss Derivatives with CDSs

by Areski Cousin of the UniversitÚ d'╔vry Val d'Essonne, and
Monique Jeanblanc of the UniversitÚ d'╔vry Val d'Essonne

February 22, 2010

Abstract: In this paper, we consider the hedging of portfolio loss derivatives using single-name credit default swaps as hedging instruments. The hedging issue is investigated in a general pure jump dynamic setting where default times are assumed to admit a joint density. In a first step, we compute default intensities adapted to the global filtration of defaults. In particular, we stress the impact of a default event on the price dynamics of non-defaulted names. In a two defaults setting, we also fully describe the hedging of a loss derivative with single name instruments. The methodology can be applied recursively to the case of a multidefault setting. We completely characterize the hedging strategies for general n-dimensional credit portfolios when default times are assumed to be ordered. The computation of the hedging strategies does not require any Markovian assumption.

Keywords: Loss derivatives, CDO tranches, Hedging, CDS.

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