Up and down credit risk

Abstract

This paper discusses the main modeling approaches that have been developed for handling portfolio credit derivatives, with a focus on the question of hedging. In particular, the so-called top, top down and bottom up approaches are considered. We give some mathematical insights regarding the fact that information, namely the choice of a relevant model filtration, is the major modeling issue. In this regard, we examine the notion of thinning that was recently advocated for the purpose of hedging a multi-name derivative by single-name derivatives. We then illustrate by means of numerical simulations (semi-static hedging experiments) why and when the portfolio loss process may not be a 'sufficient statistic' for the purpose of valuation and hedging of portfolio credit risk.