Hedging portfolio loss derivatives with CDS's

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.

On break-even correlation: the way to price structured credit derivatives by replication

“…11 thus, pricing formulas include immediate payments when default events occur during this period of time for CDX 12 , and have not been fully anticipated by the market. Moreover, our base correlations depend on the BNP-Paribas current analytics that have evolved in this period of time 13 . And, at the end of 2007, it has sometimes been difficult to find implied levels of base correlations from market quotes.…”

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

“…The reader is referred to the first chapter of Cousin et al (2009) for a thorough presentation of this method in the case of two names. Interestingly, as explained in Cousin and Jeanblanc (2010), the dynamics of portfolio loss derivatives can be fully described using the dynamics of the underlying CDS when default times are assumed to be ordered. In this particular case, the hedging strategies can be computed explicitly in a general n -dimensional framework.…”

“…To properly implement such a static hedging some kind of metrics or proximity between payoffs is required and this usually involves a model. For instance, given a joint distribution of default times in a bottom-up model, one might use a set of liquid CDO tranches to minimize the 2 ℓ -norm hedging error within a book of bespoke tranches 24 .…”

“…This can also be seen as a shift in credit spreads, often of one basis point. 24 Given a conditional (upon current information) joint distribution of default times, it is possible to compute the covariances of the bespoke payoff and of the liquid tranche payoffs and thus to derive the optimal static hedge. 25 Typically, daily or weekly data are used.…”

On break-even correlation: the way to price structured credit derivatives by replication

“…See the survey of Cousin et al (2010). Recently, Cousin and Jeanblanc (2011) have obtained general theoretical results when the underlying default events are ordered. None of these authors deals with the case of static factor models, particularly the market standard GCM.…”